LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


> 

>        ^CX/-v^ 


Class 


LTMENT, 
COAST  AND  GEODETIC  SURVEY. 


HENRY    S.    PRITCHETT, 

SUPERINTENDENT. 


SURVEYING. 


PLANE  TABLE  MANUAL. 


By   U.    B.    •WAINWRIGrHT,    Assistant. 


APPENDIX    NO.  8-REPORT    FOR    1897-98. 


WASHINGTON: 

GOVERNMENT   PRINTING   OFFICE. 
1899. 


TREASURY  DEPARTMENT, 

U.  S.  COAST  AND  GEODETIC  SURVEY. 

HENRY    S.    PRITCHETT, 

SUPERINTENDENT. 


SURVEYING. 


A  PLANE  TABLE  MANUAL. 


By    r>.    B.    WAIN  WRIGHT,    Assistant. 


APPENDIX    No.  8-REPORT    FOR    1897-98. 


WASHINGTON: 

GOVERNMENT    PRINTING    OFFICE. 
1899. 


fen 


APPENDIX    No.    8—1897-98. 


A  PLANE  TABLE  MANUAL. 


By   D.    B.    WAINWRIGHT,   Assistant. 


870 


409 


TABLE  OF  CONTENTS. 


(a)  PRELIMINARY  STATEMENT. 

Page. 

Definitions 415 

Topographical  map 415 

Projection 415 

Scale 415 

Datum  plane 415 

Relief 415 

Control 415 

(b)  INSTRUMENTS  AND  ADJUSTMENTS. 

Plane  table 416 

Description . .  .• 416 

The  board 416 

Movements 416 

Tripod 417 

Mountain  plane  table 417 

The  alidade 417 

Description 417 

Declinatoire 418 

Metal  clamps 418 

Adjustments  of  the  alidade 418 

Fiducial  edge  of  rule 418 

Level  attached  to  rule 418 

Parallax 419 

Line  of  collimation 419 

Axis  of  revolution 419 

Middle  horizontal  line 419 

Stadia  rod 420 

Description 420 

Graduation 420 

Inclined  sights 421 

Table  for  reduction  of  hypothenuse  to  base 422 

Micrometer  eyepiece 425 

Plane-table  sheet , 425 

Characteristics 425 

Distortion 425 

Scale 426 

Projections 426 

Selecting  limits 426 

Polyconic  projection 428 

Method  of  drawing 428 

Rectangular 429 

Accessories 429 

Weights 429 

411 


412  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

(c)  FIELD  WORK. 

Page. 

Organization  of  party 429 

Tableman 429 

.  Rodsmen 43° 

Aid 43° 

Preliminary  reconnoissance 43° 

Signal  poles 43° 

Graphic  triangulation 43° 

Amount  of  control 433 

Three-point  problem 433 

Advantages 433 

Definitions 434 

Lehman's  method 434 

Rule  i : 434 

Demonstration 434 

Classification 434 

Rules  2,  3,  and  4 434 

Procedure 435 

Examples  (table  deflected  to  the  right) 435 

Examples  (table  deflected  to  the  left) 435 

Repetition 435 

Orienting  by  estimation • 436 

Bessel's  method  by  inscribed  quadrilateral 436 

Tracing  cloth  protractor 437 

Two-point  problem 437 

Deflection  of  long  lines 438 

Distortion  errors 439 

Example 439 

Position  by  compromise 440 

Rules 440 

Application v 440 

Height  of  instrument 441 

Procedure 441 

Table  of  heights  (in  feet) 441 

Example  of  use  of  table 442 

Formula  for  determining  heights 442 

Table  of  heights  (in  meters) .*....  444 

Table  of  factors  for  computing  differences  in  elevation  (in  feet) 446 

Table  of  corrections  for  curvature  and  refraction  (in  feet) 447 

Table  of  factors  for  computing  differences  in  elevation  (in  meters) 448 

Table  of  corrections  for  curvature  and  refraction  (in  meters) 449 

Table;  comparison  of  feet  and  meters 449 

Relief 449 

Hill  shading r 449 

Contours 450 

Profile 450 

Advantages  and  disadvantages  of  contours  and  hill  shading 450 

Contour  interval 451 

Datum  plane 451 

Reference  signal    45 1 

Regular  and  irregular  methods  of  contouring 45 1 

Station  routine 452 

Number  of  elevations  to  be  determined 452 

Contour  sketching ».  452 


TABLE  OF  CONTENTS. 


413 


Page. 

Typical  contour  groups 453 

Order  of  development  of  contours 453 

Filling  in 453 

Traverse  lines  ....    453 

Main  traverse 454 

Subordinate  traverse 454 

Determinations  for  hydrography 454 

Low-water  mark 455 

High-water  and  storm-water  line 455 

Determination  of  inaccessible  points 455 

Large  scale  surveys , 455 

District  of  Columbia  survey ! 455 

Rapid  surveys 456 

.Military  reconnoissance  with  plane  table 456 

With  compass  and  notebook • 457 

Photogrammetry 457 

Camera  and  plane  table  in  Alaska 457 

Survey  in  advance  of  triangulation 458 

Office  work 459 


or  THE 

UNIVERSITY 

or 


APPENDIX    No.   8—1897-98. 


A   PLANE    TABLE    MANUAL 


By  D.  B.  WAINWRIGHT,  Assistant. 


a.  PRELIMINARY  STATEMENT. 

A  topographical  map  is  the  delineation  upon  a  plane  surface,  by  means  of  conven- 
tional signs,  of  the  natural  and  artificial  features  of  a  locality. 

Every  point  of  the  drawing  corresponds  to  some  geographical  position,  according 
to  some  method  adopted  for  representing  the  surface  of  the  spheroid  on  a  plane,  which 
is  called  the  projection. 

Since  it  is  a  representation  in  miniature,  the  distance  between  any  two  points  on  the 
map  is  a  certain  definite  fraction  of  the  distance  between  the  same  points  in  nature. 
This  ratio  is  called  the  scale. 

• 

Each  point,  besides  being  projected  on  a  horizontal  plane,  has  its  height,  either 
within,  above,  or  below  a  level  surface,  in  some  way  indicated.  The  level  surface 
adopted  for  the  map  is  called  the  datum  plane,  and  the  representation  of  the  variations 
in  the  vertical  element,  the  modeling  of  the  country,  is  called  the  relief. 

CONTROL. 

All  topographical  surveys  of  importance  are  based  upon  a  system  of  triangulation. 

A  sufficient  number  of  points,  whose  geographical  positions  have  been  determined 
in  this  manner,  properly  distributed  over  the  area  to  be  surveyed,  forms  a  strong  frame- 
work for  controlling  the  accurate  location  of  the  various  details.  , 

a  The  edition  of  Appendix  No.  13,  Report  of  1880,  "A  treatise  on  the  plane  table,"  by  E.  Herges- 
heinier,  Assistant,  being  exhausted,  a  new  edition  has  been  prepared  by  the  direction  of  the  Superin- 
tendent, in  which  the  material  has  been  rearranged,  some  portions  rewritten,  and  some  additions  made. 

415 


416  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

b.  INSTRUMENTS  AND  ADJUSTMENTS. 

THE   PLANE   TABLE. 

The  principal  instrument  in  use  by  the  United  States  Coast  and  Geodetic  Survey 
for  mapping  these  details  is  the  plane  table.  For  this  purpose  it  is  a  universal  instru- 
ment. All  the  necessary  operations  for  producing  a  map  are  executed  with  it  in  the 
field  and  directly  from  the  country  as  a  model. 

Other  instruments  are  employed  as  auxiliaries  to  it  under  certain  conditions,  as  will 
be  seen  later  on  under  the  head  of  "  Field  practice,"  but  in  general  it  fulfills  all  require- 
ments alone. 

Description  (PI.  i). — The  plane  table  is  composed  of  a  well-seasoned  drawing  board 
about  30  inches  in  length,  24  in  width,  three-quarters  of  an  inch  thick,  with  beveled  or 
rounded  edges.  It  is  commonly  made  of  several  pieces  of  white  pine,  tongued  and 
grooved  together,  with  the  grain  running  in  different  directions  to  prevent  warping.  It 
is  supported  upon  three  strong  brass  arms,  to  which  it  is  attached  by  screws  passing 
through  them  and  entering  the  underside  of  the  board,  the  three  holes  for  the  reception 
of  the  screws  being  guarded  by  brass  bushings  and  situated  equidistant  from  each  other 
and  from  the  center  of  the  table.  By  means  of  these  screws  the  board  can  be  removed 
at  will. 

The  movements  (Pis.  i  and  2)  of  the  tables  in  use  by  the  Coast  and  Geodetic 
Survey  are  made  from  several  different  models,  but  as  the  principal  features  are  the 
same  in  all  designs  the  description  of  one  type  will  to  a  large  extent  suffice  for  all. 

The  arms  to  which  the  board  is  fastened  rest  upon  the  sloping  upper  face  of  a  rather 
flat  hollow  cone  of  brass,  to  which  they  are  permanently  fixed.  Upon  its  lower  edge 
or  periphery  this  cone  is  fashioned  into  a  horizontally  projecting  rim,  the  inferior  face 
of  which  is  as  nearly  as  possible  a  perfect  plane,  and  this  in  its  turn  rests  upon  a 
corresponding  rim  of  somewhat  greater  diameter  projecting  slightly  beyond  it.  This 
second  rim  forms  the  upper  and  outer  flange  of  a  circular  metal  disk  in  the  form  of  a 
very  shallow  cylinder.  The  inferior  face  or  plane  of  the  upper  flange  or  rim  has,  at 
its  contact  with  the  superior  face  of  the  lower,  a  horizontal  rotary  movement  about  a 
common  center  which  is  also  the  center  of  the  instrument,  and  the  two  are  held 
together  by  means  of  a  solid  conical  axis  of  brass  extending  upward  from  the  center 
of  the  inner  face  of  the  lower  disk.  A  socket  of  similar  shape  fits  exactly  over  this 
axis,  projecting  downward  from  the  inner  side  of  the  apex  of  the  conical  or  upper 
disk.  The  two  plates  are  held  together  by  means  of  a  mill-headed  screw,  capping  the 
cone  from  the  outside,  and  which  can  be  loosened  or  removed  at  pleasure. 

A  tangent  screw  and  clamp  fastened  to  the  edge  of  the  upper  rim  permit,  when 
loose,  the  revolution  of  the  table  about  its  center,  and,  when  clamped  to  the  lower  limb, 
hold  the  table  firm  while  the  tangent  screw  gives  a  more  delicate  movement. 

Three  equidistant  vertical  projections  of  brass  grooved  on  the  underside,  and  cast 
in  one  piece  with  the  under  face  of  the  lower  disk,  extending  from  the  periphery  towar4 
the  center,  rest  upon  the  points  of  three  large  screws  which  come  through  a  heavy 
wooden  block  below.  This  block,  which  is  the  top  of  the  stand  and  is  approximate  in 
form  to  an  equilateral  triangle,  is  2^  inches  thick  when  made  of  wood. 


Coast  arul  Geodetic  Sur-vey  Report,  1897-98  Appendix  8. 


No.  2. 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  417 

The  three  screws  last  mentioned  have  large  milled  heads,  are  quite  stout,  and  play 
through  the  block  below  by  means  of  brass  female  screws  let  into  it.  They  are  the 
leveling  screws  of  the  instrument  and  are  equidistant  from  its  center. 

Upon  the  underside  and  center  of  the  metal  lower  disk  is  a  socket  containing  a 
ball  with  a  brass  arm,  which  projects  through  the  center  of  the  block  from  beneath. 
The  lower  end  of  the  arm  is  threaded,  and  upon  it  plays  a  female  screw  with  a  large 
milled  head,  which  can  be  relaxed  or  tightened  at  pleasure.  The  screw  clamps  the 
whole  upper  part  of  the  instrument  to  the  stand;  it  is  loosened  only  before  leveling 
and  kept  securely  clamped  at  all  other  times. 

The  block,  made  either  of  wood  or  brass,  is  supported  upon  three  legs,  and  with 
them  forms  the  tripod  or  stand  of  the  instrument,  the  legs  being  of  such  a  length  as  to 
bring  the  table  to  a  convenient  height  for  working,  and  so  arranged  as  to  be  taken  off 
at  will,  or  closed  so  that  their  brass  shod  and  pointed  ends  can  be  brought  together  or 
moved  outward,  as  may  be  required.  They  are  made  on  the  open  or  skeleton  pattern, 
and  each  is  securely  attached  to  a  segment  of  the  tripod  head  by  a  long  brass  bolt. 

MOUNTAIN    PLANE    TABLE. 

(PL  3-) 

A  small  plane  table,  with  a  board  measuring  only  14  by  17  inches,  is  employed  in 
•reconnaissance,  mountain  work,  or  as  an  auxiliary  to  one  of  the  standard  size.  All  the 
various  parts  are  reduced  in  size  to  correspond  with  the  board,  and  the  construction  of 
the  movement  simplified. 

THE  ALIDADE. 

The  type  of  alidade  in  general  use  (PI.  i)  consists  of  a  brass  or  steel  rule  (12  inches 
long  by  2^2  inches  wide)  nickel  plated  underneath,  from  and  perpendicular  to  which 
rises  a  brass  column  (3  inches  high),  surmounted  by  Y's,  receiving  the  transverse  axis 
of  the  telescope,  to  one  end  of  which  axis  is  firmly  attached  a  graduated  arc  of  30°, 
each  sicte  of  a  central  o° ,  an  accompanying  vernier  being  attached  to  the  lower  part  of 
the  Y  support.  The  arc  moves  with  the  telescope  as  it  is  raised  or  depressed,  and  it  is 
used  in  the  measurement  of  the  vertical  angles  for  height.  A  clamp  and  a  tangent  screw 
placed  on  the  other  side  of  the  telescope,  opposite  the  arc,  controls  its  vertical  movement. 

The  telescope  is  fitted  accurately  near  its  center  of  gravity  within  a  closely  fitting 
cylinder,  to  which  is  solidly  attached  the  transverse  axis.  The  telescope  revolves  within 
the  cylinder  180°,  stops  being  fitted  for  that  range.  This  affords  an  easy  mode  of 
adjusting  the  cross  webs  to  the  axis  of  revolution,  and  for  correction  with  a  striding 
level  of  the  errors  of  level  and  collimation  and  revolution  of  the  telescope. 

Upon  the  tube  of  the  telescope  are  turned  two  shoulders,  on  which  rest  a  striding 
spirit  level,  which  can  be  readily  reversed  or  removed  at  pleasure.  The  eye  piece 
carries  the  usual  reticule  with  screwrs  for  the  collimation  adjustment,  and  to  this  is 
attached  a  glass  diaphragm,  having  one  vertical  and  three  horizontal  lines  engraved 
upon  it.  One  of  the  horizontal  lines  crosses  the  middle  of  the  diaphragm,  the  other  two 
are  placed  equidistant  from  it,  one  above  and  one  below.  The  interval  between  them 
remains  a  constant  cnord  for  the  measurement  of  distance  upon  a  graduated  staff  or  rod. 
In  some  cases  short  auxiliary  lines  have  been  added  dividing  the  interval  into  still 
smaller  chords. 

S.  Doc.  48 27 


418  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

Several  of  the  alidades  are  furnished  with  a  micrometer  eyepiece  so  attached  that 
the  thread  is  horizontal,  and  has  a  vertical  movement  for  measuring  the  angular  distance 
of  a  fixed  length  on  a  rod  which  remains  a  constant  chord. 

To  the  rule  of  the  alidade  are  attached  two  spirit  levels,  one  in  the  longitudinal 
direction  of  the  rule  and  the  other  at  right  angles  to  it. 

The  latest  Coast  and  Geodetic  Survey  alidade  (PL  4)  differs  from  the  preceding 
type  in  having  the  vertical  arc  so  placed  that  the  vernier  can  be  read  without  the 
observer  moving  away  from  the  eye  end  of  the  telescope.  This  is  effected  by  placing 
the  arc  in  the  quadrant  nearest  the  eyepiece  and  the  graduation  of  the  arc  upon  its 
outer  periphery.  The  weight  of  this  alidade  has  also  been  reduced  by  using  aluminum 
bronze  in  its  construction,  and  by  providing  it  with  a  skeleton  rule. 

A  dedinatoire  (shown  in  Pis.  i  and  3)  accompanies  the  alidade  and  is  carried  in 
the  same  packing  box.  It  consists  of  a  rectangular  brass  box  7  inches  long  by  2  wide, 
with  an  arc  at  each  end  graduated  to  15°  on  each  side  of  the  o°.  It  contains  a  needle 
long  enough  to  extend  from  arc  to  arc,  and  resting  on  a  pivot  midway  the  box.  The 
sides  running  lengthwise  the  box  are  parallel  to  a  line  connecting  the  zero  marks  of 
the  two  graduations. 

The  metal  clamps,  for  holding  the  projection  on  the  board,  are  of  two  kinds:  The 
V-shaped  for  the  ends,  and  the  side  clamps,  the  latter-being  made  of  thin  metal  strips 
about  12  inches  in  length,  with  two  or  more  springs  to  grip  the  under  side  of  the  board.- 

THE   ADJUSTMENTS   OF  THE   ALIDADE. 

Adjustments. — From  the  nature  of  the  service  in  some  sections  of  the  country  the 
plane  table  is  often  necessarily  subjected  to  rough  usage,  and  there  is  a  constant  liability 
to  a  disturbance  of  the  adjustments;  still,  in  careful  hands,  a  well-made  instrument  may 
be  used  under  very  unfavorable  conditions  for  a  long  time  without  being  perceptibly 
affected.  One  should  not  fail,  however,  to  make  occasional  examinations,  and  while  at 
work,  if  any  difficulty  be  encountered  which  can  not  otherwise  be  accounted  for,  it 
should  lead  directly  to  a  scrutiny  of  the  adjustments. 

1.  The  fiducial  edge  of  the  rule. — This  should  be  a  true,  straight  edge.     Place  the 
rule  upon  a  smooth  surface  and  draw  a  line  along  the  edge,  marking  also  the  lines  at 
the  ends  of  the  rule.     Reverse  the  rule  and  place  the  opposite  ends  upon  the  marked 
points  and  again  draw  the  line.     If  the  two  lines  coincide  no  adjustment  is  necessary; 
if  not,  the  edge  must  be  made  true. 

There  is  one  deviation  from  a  straight  line,  which,  by  a  very  rare  possibility,  the 
•edge  of  the  ruler  might  assume,  and  yet  not  be  shown  by  the  above  test;  it  is  when  a 
part  is  convex  and  a  part  similarly  situated  at  the  other  end  concave,  in  exactly  the  same 
degree  and  proportion.  In  this  case,  on  reversal,  a  line  drawn  along  the  edge  of  the 
rule  would  be  coincident  with  the  other,  though  not  a  true  right  line;  this  can  be  tested 
by  an  exact  straight  edge. 

2.  The  levels  attached  to  the  rule. — Place  the  instrument  in  the  middle  of  the  table 
and  bring  the  bubble  of  either  level  to  the  center  by  means  of  the  leveling  screws  of  the 
table;  draw  lines  along  the  edge  and  ends  of  the  rule  upon  the  board  to  show  its  exact 
position,  then  reverse  180°.     If  the  bubble  remains  central  it  is  in  adjustment;  if  not, 
correct  it  one-half  by  means  of  the  leveling  screws  of  the  table,  and  the  other  half  by 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


419 


the  adjusting  screws  attached  to  the  level.  This  should  be  repeated  until  the  bubble 
keeps  its  central  position  whichever  way  the  rule  may  be  placed  upon  the  table.  This 
presupposes  the  plane  of  the  board  to  be  true.  The  other  level  should  now  be  examined 
and  adjusted  in  a  like  manner. 

Great  care  should  be  exercised  in  manipulation  lest  the  table  be  disturbed. 

3.  Parallax. — Move  the  eyeglass  until  the  cross  hairs  are  perfectly  distinct,  and 
then  direct  the  telescope  to  some  distant  well-defined  object.     If  the  contact  remains 
perfect  when  the  position  of  the  eye  is  changed  in  any  way,  there  is  no  parallax;  but  if 
it  does  not,  then  the  focus  of  the  object  glass  must  be  changed  until  there  is  no  displace- 
ment of  the  contact.     When  this  is  the  case  the  cross  hairs  are  in  the  common  focus  of 
the  object  and  eyeglasses.     It  may  occur  that  the  true  focus  of  the  cross  hairs  is  not 
obtained  at  first,  in  which  case  a  readjustment  is  necessary,  in  order  to  see  both  them 
and  the  object  with  equal  distinctness  and  without  parallax. 

4.  The  line  of  collimation  perpendicular  to  the  axis  of  revolution  of  the  telescope. — 
Point  the  intersection  of  the  vertical  and  the  middle  horizontal  lines  of  the  diaphragm  on 
some  well-defined    distant  object;    revolve  the  telescope  in  its  collar   180°  and  again 
observe  the  object.     If  the  intersection  covers  it,  the  adjustment  is  perfect;  if  not,  one 
half  the  error  must  be  corrected  by  moving  the  diaphragm,  by  means  of  the  adjusting 
screws,  and  the  other  half  with  the  tangent  screw  of  the  table.     This  operation  should 
be  repeated  until  the  adjustment  is  complete. 

5.  Axis  of  revolution. — Since  the  bearings  of  the  axis  are  unchangeable,  the  axis  of 
revolution  is  assumed  to  remain  parallel  to  the  plane  of  the  rule. 

6.  Middle  horizontal  line  of  diaphragm  to  the  plane  of  the  horizon. — (i)  Adjust  the 
striding-level  by  reversing  it  end  for  end  and  correcting  its  error — half  the  difference 
by  its  own  adjustment,  half  by  the  tangent-screw  of  the  telescope. 

(2)  Point  the  telescope  to  a  target,  and  note  the  reading  or  make  a  mark  where 
the  wire  points  when  the  bubble  is  in  the  middle. 

(3)  Revolve  the  telescope  about  itself,  put  the  level  on  again,  and  note  the  reading 
or  mark  the  place  where  the  telescope  now  points  when  the  bubble  is  in  the  middle. 

(4)  The  mean  of  the  two  pointings  is  the  true  level  line,  upon  which  the  wire  is 
.to  be  adjusted,  which  may  be  done  in  this  way:  Point  the  wire  to  the  mean  of  the  two 
observations  by  the  tangent-screw;  then,  by  means  of  the  adjusting-screws,  bring  it  to 
point  on  the  lower  reading,  if  the  second  reading  has  been  high,  and  vice  versa.     If  now 
brought  back  to  the  mean  by  the  tangent-screw,  the  bubble  should  be  in  its  place;  and, 
when  the  telescope  is  turned  back  into  its  first  position,  the  adjustment  should  verify. 

(5)  If  it  is  now  desired  to  make  the  vernier  read  zero  on  the  vertical  arc,  the  table 
must  be  carefully  leveled;  and  in  order  to  do  this  more  perfectly  than  can  be  done  with 
the  levels  on  the  ruler  it  may  be  done  by  observing  the  striding-level;  the  telescope 
remaining  clamped,  the  striding-level  should  read  the  same  in  every  position  of  the 
alidade  when  the  table  is  perfectly  level.     (In  general,  this  will  be  found  too  delicate  a 
test,  as  the  table  is  not  sufficiently  even  for  so  sensitive  a  level  to  be  employed.)     The 
table  being  leveled,  move  the  telescope  with  the  tangent-screw  until  the  bubble  is  in  the 
middle,  and  then  set  the  vernier  to  read  zero;  the  screw-holes  in  it  are  oblong,  so  that 
it  admits  of  being  pushed  either  way. 

(6)  It  is  easy  to  have  the  adjustments  near  enough  to  serve  for  running  curves  of 
equal  elevation,  but  in  determining  the  heights  of  stations  it  is  best  to  make  the  obser- 


420  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

vations  complete,  with  reversals,  both  of  level  and  of  telescope,  taking  the  mean  of  the 
observations,  by  which  the  errors  of  adjustment  are  eliminated.  This,  in  fact,  is 
always  done  with  the  theodolite,  and  should  be  equally  done  with  the  alidade  when 
precision  is  required. 

The  following  may  serve  as  an  example: 

TELESCOPE   DIRECT. 

Level  direct,  reading +  o°     i' 

Level  reversed,  reading o' 

Mean +  o°     o''5 

Station,  reading +-  2°  17' 

Elevation  (difference) 2°  i6'"5 

TELESCOPE   INVERTED. 

Level  direct,  reading —  o°     2' 

Level  reversed,  reading -  \' 


Mean —  o°     ix 

Station..  .  +  2°  12' 


Elevation  (difference)  2 


Mean 2°   15' 

It  will  be  seen,  from  analyzing  this  observation,  that  the  level  was  one-half  minute 
out  of  adjustment,  the  horizontal  wire  one  and  one-half  minutes,  and  that  revolving 
the  telescope  about  itself  changed  its  relation  to  the  index  on  the  vernier  by  i'.  The 
mean  is  free  from  all  errors  of  adjustment. 

The  stadia  rod*  (PI.  3),  as  used  in  the  Coast  and  Geodetic  Survey,  is  simply  a  scale 
of  equal  parts  painted  upon  a  wooden  rod  about  10  feet  long,  5  inches  wide,  and  i  ^ 
inches  thick,  so  graduated  that  the  number  of  divisions  upon  it,  as  seen  between  the 
upper  and  lower  horizontal  wires  of  the  telescope,  is  equal  to  the  number  of  units  in  the 
distance  between  the  instrument  and  the  rod  held  at  right  angles  to  the  line  of  sight. 

Graduation. — In  all  cases  the  rod  should  be  graduated  experimentally  for  the  par- 
ticular instrument,  and,  if  the  best  results  are  to  be  obtained,  to  suit  the  eye  of  the 
observer. 

In  practice  the  alidade  is  mounted  on  a  stand,  and  its  centre  (corresponding  to  the 
standard)  is  plumbed  over  one  end  of  a  hundred-metre  base,  measured  on  level  ground. 
A  line,  representing  the  zero  of  the  graduation,  having  been  drawn  about  5  inches  from 

*  It  has  been  decided  to  adopt  the  word  "stadia"  instead  of  "telemeter"  to  accord  with  the 
almost  universal  usage  of  civil  engineers  and  surveyors.  In  spite  of  its  faulty  derivation  the  former 
word  is  now  imbedded  in  the  literature  relating  to  measurements  made  according  to  this  method, 
while  the  latter  is  gradually  but  surely  disappearing.  For  further  details  of  the  theory  of  stadia 
measurements  see:  Elemente  der  Vermessungs-Kunde,  Bauernfeind,  1873,  p.  322;  Handbuch  der  Ver- 
messungs-Kunde,  Jordan,  1888,  p.  554;  Theory  and  Practice  of  Surveying,  Johnson,  1898,  p.  238; 
Gillespie's  Higher  Surveying,  Staley,  1897,  p.  311;  Experimental  Study  of  Field  Methods,  Smith, 
Bulletin  of  University  of  Wisconsin,  Engineering  series,  Vol.  I,  No.  5. 


APPENDIX  NO.  8.     PLANK  TABLE  MANUAL.  421 

one  end  of  the  rod,  the  latter  is  held  vertical  at  the  other  end  of  the  base,  zero  mark 
upward.  The  observer  at  the  alidade  then  makes  the  upper  horizontal  line  of  the 
diaphragm  coincide  with  the  zero  and  directs  the  rodsman  by  signals  where  to  draw  a 
line  which  coincides  with  the  lower  horizontal  line.  This  intercepted  space  on  the  rod 
is  now  subdivided  into  the  smaller  parts  of  the  adopted  scale  and  the  graduation  con- 
tinued to  within  a  short  distance  of  the  bottom. 

This  graduation  is  represented  by  the  equation 


where  </  =  the  distance  from  the  centre  of  instrument  to  rod  (in  this  case  100  metres); 
/=the  focal  length  of  the  telescope  (which  is  35cm  for  the  average  alidade); 
i  =the  distance  between  the  upper  and  lower  wires  of  the  diaphragm  (4"""); 
,y=the  length  of  the  intercepted  portion  of  the  rod  (i'i85m); 

f     f     35cm  A 

c  =  the  distance  from  object  glass  to  center  of  instrument  ^  ==—  =  -  generally  ) 

As  indicated  in  the  preceding  equation,  the  readings  of  a  rod  graduated  in  this 
manner  are  not  quite  true  for  distances  above  or  below  100  metres,  since  the  vertices  of 
the  constant  and  similar  angles  (one  subtending  the  chord  represented  by  the  inter- 
cepted space  011  the  rod  and  the  other  by  the  space  between  the  upper  and  lower  wires) 
do  not  lie  at  the  centre  of  the  instrument,  but  at  a  distance  beyond  the  object  glass 
equal  to  the  focal  length  of  the  telescope,  and  therefore  the  intercept  on  the  rod  will  not 
be  proportional  for  all  distances  from  the  centre  of  the  instrument.  To  have  it  so  the 
instrument  should  be  mounted  at  a  distance  back  from  the  end  of  the  base  equal  to  one 
and  a  half  times  the  focal  length  of  the  telescope  (,f-\-c).  To  all  readings  of  a  rod 
graduated  according  to  this  last  method  the  constant  quantity  f-\-c  must  be  added. 

The  correction  for  the  first  method  is  small  and  can  be  ignored  for  mapping  on  a 
scale  of  i-io  ooo  or  smaller. 

The  formula  for  the  correction  is: 


\Yhere  K=  correction  in  meters, 

B  —  distance  read  on  rod  in  meters, 

B'  —  length  of  base,  in  meters,  for  which  the  rod  was  graduated. 

The   corrections   for  50,  200,  300,  and  400  meters  are  +  o'262,  —  o'525,  — 
—  i  '575  meters,  respectively. 

Inclined  sights.  —  The  foregoing  applies  only  to  horizontal  sights.  When  the  rod 
is  held  at  a  point  above  or  below  the  instrument,  the  line  of  sight  is  inclined  at  an  angle 
with  the  horizon,  and  a  correction  has  to  be  applied  to  the  reading  to  obtain  the  hori- 
zontal distance.  Some  observers  prefer  to  have  the  rod  held  perpendicular  to  the  line 
of  sight,  the  reduction  then  being  simply  the  cosine  of  the  angle  of  inclination  into  the 
rod  reading;  the  small  correction  for  the  difference  in  horizontal  distance  between  the 
point  where  the  line  of  sight  cuts  the  rod  and  the  foot  of  the  rod,  being  ignored. 

The  latter  correction  is: 

Vertical  angle  :     50  m  :   100  m  :  200  in. 

5°  :  +0-23  :  +o'2i  :  +  0-15 

10°  :  +0-48  :  +0-43  :  +0-33 


422  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98.     • 

For  the  reduction  of  the  hypottienuse  to  the  base,  the  following  table  is  given: 
Table  for  reduction  of  hypothemise  to  base. 


Hypothenuse. 

too  meters. 

200  meters. 

300  meters. 

400  meters. 

500  meters. 

5° 

99-62 

199-24 

298-86 

398-48 

498-10 

10° 

98-48 

196-96 

295-44 

393-92 

492-40 

15° 

96-59 

I93'I9 

289-78 

386-37 

482-96 

20° 

93  '97 

187-94 

281-91 

375-88 

469-85 

25° 

90-63 

181-26 

271-89 

362-52 

453-I5 

30° 

86-60 

173-21 

259-81 

346-4I 

433-0! 

35° 

81-92 

163-83 

245-75 

327-66 

409-58 

40° 

76-60 

I53-2I 

229-81 

306-42 

383-02 

45° 

70-71 

141-42 

212-13 

282-84 

353-55 

With  the  preceding  method  a  sight  must  be  attached  to  the  rod,  or  the  amount  of 
inclination  left  to  the  judgment  of  the  rodsman.  An  objection  to  it  becomes  evident 
when  it  is  necessary  to  measure  the  vertical  angles  of  the  back  and  foresight,  since  the 
rod  changes  its  inclination  with  each  new  position  of  the  instrument. 

A  second  method  is  one  where  the  rod  is  always  held  vertical.  Here  besides  the 
correction  to  reduce  the  inclined  distance  to  a  horizontal  one,  an  additional  one  must 
be  applied  for  the  oblique  view  of  the  rod. 

The  equation  for  reducing  the  readings  is: 

Horizontal  distance =r  cos2  v-\-(c-\-f~)  cos  v 

Where  rereading  of  vertical  rod; 

v = angle  of  elevation  or  depression; 
c=  distance  of  object  glass  to  center  of  instrument; 
y= focal  length  of  telescope. 

The  following  table  gives  the  coefficient  of  reduction  by  which  the  rod  reading  is 
to  be  multiplied.  It  is  based  on  the  assumption  that  c-\-f  is  to  be  added  to  the  result 
to  obtain  the  distance  to  the  center  of  the  instrument. 

Example:  Given  an  angle  of  elevation  or  depression  8°  10'  and  the  reading  of  the 
inclined  sight  on  vertical  rod  =173*1  meters. 
From  the  table: 

Factor  for  i     metre  for  8°  10'  multiplied  by  100=97-98  meters. 

"       "   7         "       "    "  "  "  "     10=68-59      " 

"3  '   "  "    =  2-94     " 

"       "   o-i      "       "    "  "     =     -09      " 


.  Horizontal  distance 169-60 

To  which  H-/is  to  be  added. 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


423 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  vertical  rod  to  horizontal 

distance* 


Angle  of 
inclina- 
tion 

Horizontal  projection  of  : 

i  m 

2  m 

3  ni 

4  m 

S  111 

6  m 

;m 

8  m 

9  in 

0°  I0/ 
20' 
30; 
40' 
50' 

"99999 
'99997 
•99992 
•99986 
•99979 

1-99998 
1-99993 
1-99984 
1-99973 

i  '9995  7 

2-99997 
2-99990 
2-99977 
2-99959 
2-99936 

3-99997   4-99996 
3-99986   4-99983 
3-99969   4-99962 
3-99946   4-99932 
3"999!5   4-99894 

5  '99994 
5-99980 

5-99954 
5'999J9 
5-99873 

6-99994 
6-99977 
6-99946 
6-99905 
6-99852 

7*99993 
7*99973 
7*99939 
7-99892 
7-99831 

8*99993 
8-99970 
8-99932 
8-99878 
8*99810 

1°  OO' 

•99970 

i  '99939 

2-99909   3-99878 

4-99848   5-99817 

6-99787 

7*99757 

8*99726 

10' 
2O/ 
30' 

4P> 
5^ 

'99959 
•99946 
•99932 

•99915 
•99908 

1-99917 
1-99891 
1-99863 
1-99831 
1-99801 

2-99875 
2-99838 
2-99794 
2-99746 
2-99693 

3-99834 
3-99783 

3  '997  25 
3'99659 
3  '99590 

4'99793 
4-99729 

4'99657 
4'99572 
4-99488 

5-99752 
5-99676 
5-99589 
5'99489 
5  '99386 

6-99711 
6-99622 
6-99520 
6-99406 
6-99284 

7-99669 
7-99568 
7-99452 
7-99323 
7-99182 

8-99628 
8-99514 
8-99384 

8-99239 
8-99080 

2°00/ 

•99878 

1-99756 

2  '99635  i  3  '995  13 

4'9939* 

5-99269 

6-99147 

7-99025 

8-98904 

io" 

20' 
30' 
40' 
50' 

•99857 
•99834 
•99810 
•99784 
•99756 

1-99714 
1-99669 
1-99620 
1-99568 
1-99511 

2'9957i 
2'99503 
2-99429 

2'9935i 
2-99267 

3-99428 
3  '99337 
3  '99239 
3'99i35 
3-99023 

4-99285 
4-99171 
4-99049 
4-98918 
4-98778 

5-99142 
5-99006 

5-98859 
5-98702 

5  '98534 

6-99000 

6-98840 
6-98669 
6-98485 
6-98290 

7*98857 
7-98675 
7-98479 
7-98268 
7-98046 

8-98714 
8-98509 
8-98289 

8-98053 
8-97802 

3°oo/ 

•99726 

1-99452 

2-99178 

3-98904 

4-98630 

5'98357 

6-98083 

7-97809 

8-97635 

10' 

20' 

30' 
40' 
5o/ 

•99695 
•99662 
•99627 
•99591 
'99553 

1-99390 
1-99324 

i  '99255 
1-99182 
1-99106 

2-99085 
2-98986 
2-98882 
2-98773 
2-98659 

3-98780 
3-98648 
3'98509 
3  '98364 
3-98212 

4-98474 
4-98309 
4-98136 
4'97955 
4^7765 

5-98169 
5'97972 
5  '97764 
5-97546 
5'973i8 

6-97865 
6-97634 
6-97391 
6-97137 
6-96871 

7*9756o 
7-97296 
7-97019 
7-96728 
7-96424 

8-97255 
8-96958 
8-96646 
8-96319 
8-95978 

4°  oo' 

•99513 

1-99027 

2-98540 

3  '98054 

4'97567 

5-97081 

6-96595 

7-96108 

8-95621 

10' 
2OX 

3^ 

40' 
50' 

•99472 
•99429 
•99384 
•99338 
•99290 

1-98944 
1-98858 
i  "98769 
i  -98676 
1-98580 

2-98416 
2-98287 
2-98153 
2-98014 
2-97870 

3-97888 
3-97716 
3-97537 
3-97352 
3-97160 

4-97360 

4'97i45 
4-96922 
4-96690 
4-96450 

5-96832 

5'96574 
5-96306 
5-96028 
5  '95  740 

6-96304 
6-96003 
6-95691 
6-95366 
6-95030 

7*95776 
7*95432 
7*95075 
7-94704 
t  7-94320 

8-95249 
8-94862 
8-94460 

8-94043 
8-93611 

5°  oo' 

•99240 

1-98481 

2-97721 

3-96961 

4-96202 

t  5  '95443 

6-94683 

7-93923 

8-93164 

10' 
2OX 
30' 

40' 
So7 

•99189 
•99136 
•99081 
•99025 
•98967 

1-98378   2-97567 
1-98272   2-97408 
1-98163   2-97244 
1-98050   2-97075 
1-97934   2-96901 

3'96756 
3'96544 
3-96326 
3'9t>ioo 
3-95868 

4'95945 
4-95680 

4  '95407 
4  '95  1  25 
4  '94835 

5  '95  134 

5-94816 

5  '94489 
5  '94  1  50 
5-93802 

6-94323 
6-93952 
6-93570 
6-93I75 
6-92769 

7-93512 
7-93088 
7-92652 
7-92200 
7-91736 

8*92702 
8-92224 

8-9I733 
8-91225 
8-90703 

6°  oo' 

•98907 

1-97814   2-96722 

3  '95630 

4*94537 

5  '93445 

6-92358 

7-91260 

8-90167 

10' 

2O' 

30' 
40' 
50' 

•98846 

•98783 
•98718 
•98652 
•98584 

1-97692 
1-97566 
1-97436 
1-97304 
1-97169 

2-96538 
2-9.6349 
2-96155 
2-95956 
2-95753 

3'95384 
3-95I32 
3'94873 
3-94609 

3'94337 

4-94230 
4'939J5 
4'9359* 
4-93261 
4-92921 

5  '93077 
5-92698 
5-92310 

5'9i9!3 
5*9J5o6 

6-91923 
6-91481 
6-91029 
6-90566 
6-90090 

7-90769 
7-90264 
7-89748 
7-89218 
7-88674 

8-89615 
8-89048 
8-88467 
8-87870 
8-87259 

7°oo' 

•98515 

1-97030 

2-95544 

3'94059 

4'92574 

5-91089 

6-89604 

7-88119 

8-86634 

*  Furnished  by  J.  A.  Flemer,  Assistant,  Coast  and  Geodetic  Survey. 


424 


COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  vertical  rod  to  horizontal 

distance — Continued. 


Angle  of 
inclina- 
tion. 

Horizontal  projection  of  : 

i  m 

2   111 

3  ^^ 

4  in 

5« 

6  ill 

7  m 

8  m 

9  m 

10' 

20' 
30' 
40' 
50' 

•98444 
•98371 
•98296 
•98220 
•98142 

I-96888 
I-96742 
I-96592 
I  -96441 
I-96285 

2-95331 
2-95112 
2-94889 
2-94661 
2-94427 

3'93775 
3  '93483 
3-93I85 
3-92881 
3-92570 

4-92218 
4-91854 
4-91481 
4-91101 
4-90712 

5-90662 

5-90225 

5-89322 
5-88855 

6-89105 
6-88596 
6-88073 
6-87542 
6-86997 

7-86967 
7-86370 
7-85762 
7-85140 

8-85993 
8-85337 
8-84667 
8-83982 
8-83282 

8°  oo' 

•98063 

I-96I26 

2-94189 

3-92252 

4-903I5 

5-88378 

6-86441 

7-84504 

8-82568 

10' 

20' 
30' 
40' 
50' 

9°oo' 

•97982 
•97899 

•97815 
•97729 
•97642 

r95964 

I  '95798 
I-95630 

i  '95459 
1-95284 

2-93946 
2-93698 
2-93446 
2-93188 
2-92926 

3-91928 
3-9'598 
3-91261 
3-90918 
3-90568 

4-89910 

4-89497 
4-89076 
4-88647 
4-88209 

5^7892 
5-86891 
5-8585I 

6-85874 
6-85296 
6-84707 
6-84106 
"6-83493 

7-83196 
7-82522 
7-81836 
7-81134 

8-81839 
8-81096 
8-80337 

879565 

8-78777 

'97553 

1-95106 

2-92658 

3-90211 

4-87764 

5-853I7 

6-82870 

7-80423 

877975 

10' 

20' 

3</ 

50' 

•97462 
•97370 
•97276 
•97180 
•97083 

1-94924 
1-94740 
i  '94552 
1-94361 
1-94166 

2-92386 
2-92110 
2-91828 
2-91542 
2-91250 

3-89848 
3-89480 
3-89104 
3-88722 
3-88333 

4-87310 
4-86849 
4-86379 
4-85902 
4-85416 

5^4772 
5-84219 

5-83083 
5-82499 

6-82234 
6-81589 
6*80931 
6-80263 
6-79583 

779696 

778959 
7-78207 

777444 
7-76667 

877159 
8-76328 

8-74624 
8-73750 

10°  OO' 

•96985 

i  -93970 

2-90954 

3-87938 

4-84923 

5-81907 

6-78892 

7-75876        8-72861 

10' 

20' 

30' 

40' 
50' 

•96884 
•96782 
•96679 
•96574 
•96467 

1-93769 
i'93565 
i  '93358 
1-93148 
1-92934 

2-90653 
2-90347 
2-90037 
2-89721 
2-89402 

3-87129 
3-86716 
3-86295 
3-85869 

4-84421 
4-83912 

4'83395 
4-82869 
4-82336 

5-81306 
5-80695 
5-80074 

S'79443 
5-78803 

6-78190 
6-77477 

676753 
6-76017 
6-75271 

7750/4 
774259 
773432 
7-72591 
7-71738 

8'7I959 
8-71042 
8-70111 
8-69165 
8-68206 

11°  OO' 

•96359 

1-92718 

2-89077 

3-85436 

4  '8  1  795 

5-78I54 

6-745I3 

7-70872        8-67232 

10' 

20' 
30' 
40; 

•96249 
•96138 
•96025 

•959" 
'95795 

i  '92498 
1-92276 
1-92051 
1-91822 
1-91590 

2-88748 
2-88414 
2-88076 
2-87732 

3-84997 
3-84552 
3.84101 

3-83643 
3-83180 

4-81247 
4-80690 
4-80126 

479553 
4-78974 

5-76828 
5-76I52 
5-75464 

6-73746 
6-72966 
6-72177 

6-7I375 
6-70564 

7-69995        8-66245 
7-69104        8-65242 
7-68202        8-64227 
•  7-67286        8-63196 
7-66358        8-62153 

I2°00' 

•95677 

I-9I355 

2-87032 

3,82709 

4-78386 

5-74063 

6-69741 

7-65418        8-61095 

10' 

2O' 

iv 

50' 

•95558 
•95438 
•95315 
•95192 
-95066 

1-91116 

i  -90876 
1-90631 
1-90384 
1-90132 

2-86674 
2-86313 
2-85946 

2-85575 
2-85199 

3-82232 
3-81750 
3-81261 
3-80766 
3-80265 

4-77790 
4-77187 
4-76576 
475958 

5-72625 
5-71892 
57H50 
5-70399 

6-68906 
6-68062 
6-67207 
6-66341 
6-65465 

7-64464 
7.63500 
7-62522 

7-6I533 
7-60532 

8-60023 
8-58938 
8-57838 
8-56724 

8-55598 

13°  oo' 

10' 

20' 
30' 
40' 
50' 

•94940 

i  -89880 

2-84820 

3-79759 

4-74698 

5-69638 

6-64577      7'595i6        8-54456 

•9481  1 
•94682 
"94550 

"94417 
•94283 

1-89623 
i  -89364 
1-89101 
1-88835 
1-88566 

2-84434 
2-84045 
2-83651 
2-83252 
2-82849 

3-79245 
3-78726 
3-78201 
3-77669 

4-74056 
473407 
472751 
4-72087 

47I4I5 

5-68868 
5-68088 

5'66505 
5-65698 

6-63679      7-58491   ;      8-53302 
6-62770      7-57452        8-52133 
6-61852      7-56402        8-50952 
6-60922      7-55339        8-49757 
6-59981      7-54264        8-48548 

14°  oo' 

•94147 

1-88295 

2-82442    3-76589 

4-70736 

5-64884 

6*59031       7  '53  i  79        8-47326 

APPENDIX  NO.  S.     PLANE  TABLE  MANl'AL. 


425 


Table  of  coefficients  for  reducing  readings  of  inclined  sights  on  vertical  rod  to  horizontal 

distance — Continued. 


Angle  of 
inclina- 
tion. 

Horizontal  projection  of  : 

i  m 

2  m 

3  m 

4  ni 

5  in 

6  m 

7  m 

S  m 

9  in 

I0/ 

20' 

30' 

40' 
50' 

•94010 
•93871 
•93731 
•93589 
•93446 

1-88020 
1-87742 
1-87462 
1-87178 
1-86892 

2  '82030 
2-8l6l3 
2-81192 

2-80767 
2-80338 

3-76040 
375484 
374923 
374356 
373784 

4-70050 

4"69355 
4-68654 

4-67945 
4-67229 

5-64060 
5-63226 
5-62385 
5-6I534 
5  '60675 

6-58070 
6-57097 
6-56II5 
6-55I23 
6-54121 

7-52080 
7-50968 
7-49846 
7-48712 
7'47567 

8-46090 
8-44840 

8-43578 
8-42302 
8-41013 

15°  ex/ 

•93301 

1-86602 

2-79903 

.373204 

4-66505 

5-59806 

6-53I07 

7-46408 

8-39710 

16°  oo' 

•92402 

1-84805 

2-77208 

3-69610 

4-62011 

5"544I4 

6-46816 

7-39218 

8-31620 

17°  oo' 

'9!452 

I  '82904 

2-74355 

3-65806 

4'57258 

5-48710 

6-40161 

7-3I6I3 

8-23065 

i8°oo' 

•90451 

1-80902 

271352 

3-61803 

4-52253 

5  '42704 

6-33I54 

7-23605 

8-14056 

19°  oo' 

•89400 

1-78800 

2-68201 

3-57600 

4-47001 

5'36402 

6-25802 

7-15203 

8-04603 

20°  OO' 

•88302 

1-76604 

2-64906 

3  '53208 

4-41510 

5-29812 

6-18114 

7-06416 

7-94718 

Micrometer  eyepiece. — Where  a  micrometer  eyepiece  is  used  in  place  of  the  stadia 
lines,  a  rod  about  3*7  meters  in  length  is  employed,  attached  to  which  are  two  targets. 
A  base  is  measured  on  level  ground  and  the  instrument  either  plumbed  over  one  end  or 
back  of  it  a  distance  equal  to/  +  c,  depending  upon  the  manner  the  rod  is  to  be  held 
for  an  inclined  sight.  The  rod  is  then  taken  to  one  of  the  subdivisions  of  the  base, 
consisting  of  an  even  multiple  of  the  unit  adopted;  say  100,  200,  or  300  meters,  and 
the  upper  target  being  fixed,  the  lower  target  is  set  and  fixed  so  that  the  angular  meas- 
ure of  the  interval  by  the  micrometer  will  consist  of  an  even  multiple  of  turns  of  the 
micrometer  screw.  The  rod  is  now  held  at  the  other  subdivision  of  the  base,  and  the 
readings  tabulated.  A  distance  table  is  then  prepared,  by  interpolation,  for  the  inter- 
mediate distances. 

Plane-table  sheet. — From  the  standpoint  of  efficiency  the  plane-table  sheet  is  the 
least  satisfactory  portion  of  the  plane  table  equipment.  Owing  to  its  hygrometric  nature 
it  is  very  susceptible  to  atmospheric  changes;  expanding  and  contracting  unceasingly. 
This  would  be  but  an  insignificant  source  of  error  or  annoyance  if  it  were  equal  in  all 
directions.  The  map  or  plan  would  then  simply  change  its  scale,  for  which  an  allowance 
could  readily  be  made.  But  the  objectionable  feature  arises  from  the  unequal  expan- 
sion and  contraction  which  changes  the  relative  distance  and  directions  of  the  points. 
It  has  been  determined  by  experiment  that  strips  cut  longitudinally  from  drawing  paper 
varied  from  10  to  25  per  cent  more  than  strips  cut  transversely  from  the  same  paper. 

Various  substitutes*  have  been  tried,  but  none  have  proved  entirely  satisfactory. 
The  United  States  Geological  Survey,  to  eliminate  this  distortion,  employs  two  sheets 
of  paragon  paper,  the  size  of  the  plane-table  board,  mounted  with  the  grain  at  right 
angles,  and  with  cloth  between  them. 

*  Celluloid  sheets  are  frequently  used  in  Alaska.  The  pencil  lines  are  neither  washed  out  nor 
blurred  by  water  accumulating  on  the  sheet. 


426  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

This  method  is  applicable  to  small  scale  surveys  where  a  sheet  the  size  of  the  table 
board  covers  a  large  area  of  country,  or  on  the  other  hand,  to  large  scale  cadastral  sur- 
veys where  the  great  amount  of  detail  makes  the  rate  of  progress  slow.  '  But  for  inter- 
mediate scales  and  an  area  containing  a  moderate  amount  of  detail,  a  longer  sheet  is 
much  more  economical,  because  a  smaller  number  of  points  are  needed  to  inclose  the 
work  within  the  control  of  the  triangulation  than  would  be  required  if  it  was  limited 
to  the  size  of  the  table.  A  certain  amount  of  overlapping  work,  of  which  there  is  more 
or  less  at  the  junction  of  the  two  sheets,  would  also  be  avoided. 

The  plane-table  sheet  of  the  United  States  Coast  and  Geodetic  Survey  consists  of  a 
sheet  of  Whatman's  cold -pressed  hand- made  antiquarian  paper,  52  by  30  inches.  It  is 
backed  with  muslin,  which  extends  about  i  inch  beyond  the  edge  of  the  paper  to  pro- 
tect it  from  fraying. 

To  reduce  the  distortion  to  a  minimum  a  sheet  should  be  thoroughly  seasoned  before 
it  is  taken  to  the  field  or  a  projection  laid  down  on  it.  This  is  effected  by  exposing  it 
alternately  to  a  very  damp  and  a  very  dry  atmosphere.  On  testing  a  sheet  after  a  week 
of  such  exposure  it  will  be  found  to  have  much  less  tendency  to  expand  or  con- 
tract unequally. 

Paper  stored  away,  piled  up  in  stacks,  does  not  properly  season. 

Scale. — The  selection  of  the  scale  to  be  employed  depends  so  much  on  the  char- 
acter of  the  country  to  be  surveyed,  the  amount  of  detail  to  be  included,  and  the  uses  to 
which  the  completed  map  will  be  put,  that  no  general  rule  can  be  given  for  guidance. 
It  must  be  remembered,  however,  that  nothing  is  gained,  either  in  economy  or  rapidity, 
by  the  use  of  small  scales  when  the  details  to  be  shown  are  plentiful.  The  minute 
drawing  involved  proves  a  tax  on  the  topographer  and  is  a  great  time  consumer. 

The  scale  adopted  by  the  Coast  and  Geodetic  Survey  for  the  coast  line  from  Maine 
to  Delaware  Bay  is  i-io  ooo;  from  Delaware  Bay  southward,  1-20  ooo.  Special  sur- 
veys have  been  made  on  a  scale  as  large  as  i-i  200. 

PROJECTIONS    FOR    FIELD   SHEETS. 

It  is  presumed  that  determination  has  been  made,  by  triangulation,  of  points  most 
suitable  for  the  use  of  the  topographer  who  follows  with  the  plane-table  work,  and  that 
a  sketch  of  the  same  is  at  hand,  giving  an  approximate  skeleton  map  of  the  area  to  be 
surveyed.  The  location  or  orientation  (as  it  is  frequently  called)  of  the  sheet  is  then 
based  upon  several  important  considerations. 

It  may  be  taken  as  a  rule  that  the  intervisibility  of  the  points  extends  across  valleys, 
from  summit  to  summit,  or  across  rivers,  bays,  and  other  bodies  of  water  So  that 
generally  the  line  of  greatest  depression  of  the  valley  (thalweg)  should  follow  as  nearly 
as  practicable  the  middle  of  the  sheet,  regard  being  had  for  any  abrupt  change  of  direc- 
tion or  importance  of  lateral  features;  or,  in  other  words,  the  areas  to  be  surveyed 
should  be  divided  as  far  as  possible  into  water  basins,  extending  from  divide  to  divide, 
and  not  center  upon  a  ridge  forming  portions  of  two  basins.  The  reason  for  this  being, 
that  from  either  slope  of  the  basin  points  are  visible  on  the  opposite  summits  which  will 
be  common  to  the  sheets  which  include  the  adjoining  valleys,  while  from  the  middle  of 
the  valley  points  will  be  visible  on  both  summits. 


li 

i 

i 

J 

s 

$ 

IP 

a 

i. 

0 

\ 
\ 

'! 

i 
i 

a 

x 

i 
j- 

1 

1 

" 

i 
i 

i 

i 
i 

^ 

^i      «5 

/I- 

! 

i 

"*A 

fl 

fc      .$ 

II 

ae 

V 
1 

u 

B 

*ij 

i 
i 
i 

i 
i 

i 

^ 

^11 
«  "S   * 

i 

s 

~"^^-"^ 
f 

« 

"  if! 

|*«   H 

"§    §     o 

K        «         «3 

jT 

i 

'     ft1 

^    S 

2     8 

0 

v5     O 

.8  4> 

«    =><e 
1       1 

. 

W 

N 

X 

nil 

'! 

r 

* 

OQ 

a 

$ 

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) 

APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  427 

From  the  written  descriptions  of  the  points  determined,  discrimination  should  be 
made  in  regard  to  their  temporary  or  permanent  character.  A  flag  in  a  tree  is  likely  to 
have  disappeared  soon  after  its  determination,  and  the  usual  cut  of  a  triangle  in  its  bark 
may  have  disappeared  before  the  lumberman's  ax,  while  a  church  spire,  a  light-house, 
a  house  chimney,  a  copper  bolt  in  a  rock,  or  a  bottle  buried  beneath  the  surface  of  the 
ground  is  more  likely  to  be  recovered  and  to  be  of  service  to  the  topographer. 

Two  intervisible  points,  one  of  which  may  be  occupied,  or  three  inaccessible  points, 
are  all  that  are  absolutely  necessary  upon  a  sheet  for  the  commencement  of  work,  for 
from,  or  upon  these,  all  other  points  required  may  be  determined,  and  it  is  oftener 
more  important,  from  considerations  of  economy  of  time  and  facility  for  work,  to  have 
more  regard  for  comprising  the  topographical  subject  in  its  entirety,  where  points 
may  be  determined  at  convenience,  than  to  furnish  a  large  number  of  determined 
points  at  the  expense  of  the  best  orientation  of  the  sheets  in  regard  to  topographical 
details. 

In  flat  sections  where  the  vertical  question  is  scarcely  a  factor,  the  main  ques- 
tion is  generally  a  plan  that  will  comprise  the  area  with  the  fewest  sheets  compatible 
with  a  sufficient  overlap  of  common  points;  and  where  the  object  is  a  survey  of  one  side 
of  a  river  or  other  body  of  water,  points  on  the  opposite  shore  should  be  included  where 
possible. 

Where  it  is  possible,  the  sheet  should  be  located  by  one  familar  with  the  peculiar 
topography  of  the  region  to  be  surveyed,  and  with  some  knowledge  from  observation 
of  the  relative  value  of  the  points  between  which  there  may  be  any  necessity  for 
discrimination. 

Where  the  surface  is  broken  without  any  marked  basins  of  large  area,  and  when 
the  sheet,  on  the  scale  determined  upon,  will  comprise  several  successive  basins  and 
dividing  ridges,  the  consideration  of  reach  from  higher  to  higher  summits  should  control 
as  in  the  reach  over  one  valley;  thereby  affording  the  best  means  for  determining  posi- 
tion and  any  desirable  auxiliary  points  in  the  lower  intermediate  summits  and  in  the 
valleys. 

Points  at  the  junction  of  confluent  streams  have  usually  large  arcs  of  visibility,  and 
are  consequently  of  great  value  for  purposes  of  orientation.  If,  therefore,  such  a  point 
should  be  near  but  off  the  edge  of  a  sheet  of  regular  dimensions,  and  from  the  necessi- 
ties at  the  opposite  edge  can  not  be  included  by  it,,  it  is  often  well  to  extend  the  length 
of  the  sheet  so  as  to  include  the  point,  even  though  there  may  be  no  intention  to  com- 
plete topographical  details  upon  the  additional  piece. 

Light-houses  are  often  of  this  character,  the  reasons  governing  the  selection  of  their 
positions  for  light  purposes  having  equal  weight  in  the  selection  of  such  positions  for 
survey  signals. 

The  draftsman  will  be  materially  assisted  in  laying  out  the  limits  of  the  projection 
by  drawing  on  a  piece  of  tracing  vellum  a  plan  of  the  sheet,  corresponding  in  size  to  the 
scale  of  the  triangulation  sketch.  Take,  for  example,  a  sheet  52  inches  in  length  by  30 
in  width,  on  which  a  projection  on  a  scale  of  i-io  ooo  is  to  be  drawn,  the  triangulation 
sketch  being  on  a  scale  of  i-ioo  ooo.  The  dimensions  of  the  plan  will  then  be  one- 
tenth  those  of  the  sheet,  viz,  5.2  by  3.0  inches.  Placing  the  pattern  over  the  sketch 
and  shifting  its  position  about  over  the  locality  to  be  surveyed,  the  limits  which  include 
the  most  favorable  conditions  for  the  projection  will  soon  become  apparent. 


428  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

The  Poly  conic  projection*  has  been  adopted  by  the  Coast  and  Geodetic  Survey  for 
mapping  its  work.  The  method  of  drawing  one  is  as  follows: 

The  limits  of  the  sheet  having  been  determined,  the  middle  meridian  A  (see  PI.  5) 
is  located  and  drawn;  then  its  intersection  with  the  most  central  parallel  is  found,  and 
the  perpendicular  B  erected  there. 

Next  turn  to  the  page  of  the  "  Polyconic  projection  tables"  f  in  which  is  given  the 
degree  of  latitude  which  includes  the  limits  of  the  sheet.  In  this  instance  the  latitude 
is  40°,  to  be  found  on  page  223  of  the  tables.  The  number  of  minutes  of  latitude  on  the 
central  meridian,  above  and  below  the  central  parallel,  being  known,  take  the  correspond- 
ing distance  from  the  column  headed  ' '  Sums  of  minutes  for  middle  latitude ' '  and  lay  it 
off  (C)  above  and  below  the  central  parallel,  and  with  the  same  distance  as  radius, 
strike  arcs  D  D  D  D  above  and  below,  from  near  the  extremities  of  the  perpendicular 
B.  With  a  well-tested  straightedge  draw  lines  E  E  through  the  north  and  south 
minutes  on  the  central  meridian,  and  tangent  to  the  two  arcs  D  D  to  the  right  and  left. 
This  gives  three  parallel  lines  perpendicular  to  the  central  meridian.  On  the  opposite 
page  222,  from  under  the  head  of  "Arcs  of  the  parallel  in  meters,"  take  out  the  value 
corresponding  to  the  number  of  minutes  of  longitude  east  and  west  of  the  central 
meridian  and  lay  off  the  whole  distance .  F  F'  F"  on  each  perpendicular,  taking  each 
distance  from  its  appropriate  latitude.  Subdivide  these  into  minutes  G  G'  G". 

For  the  areas  usually  covered  by  plane-table  sheets  the  corrections  X,  for  deter- 
mining the  abscissas  from  the  arcs  of  parallels  (Table  VI,  head  "  Coordinates  of  curv- 
ature"), are  inappreciable,  and  may  be  disregarded;  the  ordinates  Y  only  being  used. 
These  give  the  distances  to  be  set  off  from  the  lines  Band  E,  perpendicularly  toward*  the  pole, 
for  each  minute  of  longitude  counting  from  the  central  meridian.  For  ordinary  field 
projections  of  scale  TO-VTTT  the  ordinate  of  the  extreme  minute  only  need  be  used,  and 
the  parallel  drawn  a  right  line  from  the  point  so  found  to  the  central  meridian.  This 
ordinate  H  being  set  off  on  each  of  the  parallels,  the  meridians  are  all  drawn  in  with  a 
fine  ruling  pen,  then  subdivided  into  minutes,  and  the  parallels  carefully  ruled  in 
through  the  points  of  subdivision. 

The  projection  is  verified  by  applying  the  measure  of  a  number  of  minutes  of  lati- 
tude and  longitude,  and  by  a  comparison  of  diagonal  measurements  on  different  parts 
of  the  sheet. 

AH  measurements  should  be  carefully  taken  from  the  scale  with  a '  keenly  pointed 
beam-compass,  and  the  marks  pricked  in  the  paper  should  be  as  light  as  possible  to  be 
seen,  so  as  to  insure  the  greatest  possible  accuracy. 

The  draftsman  is  supplied  with  a  list  of  triangulation  points,  which  gives  their  rel- 
ative distances,  their  latitudes  and  longitudes,  and  also  the  equivalents  in  meters  of  the 
seconds  of  latitude  and  longitude,  according  to  which  the  points  are  now  plotted  on  the 
sheet  by  measuring  from  the  corresponding  minutes.  Thus  in  the  diagram  the  distance 
J  represents  the  seconds  of  latitude;  K,  the  seconds  of  longitude  of  the  trigonometrical 
point. 

The  accuracy  of  the  plotting  is  tested  by  a  measurement  of  the  respective  dis- 
tances between  the  points  with  a  beam-compass,  these  distances  being  also  given.  The 

*  See  a  Treatise  on  Projections,  Craig,  United  States  Coast  and  Geodetic  Survey  Bulletin,  1882. 
Chart  and  Chart  Making,  Pillsbury,  No.  29,  Proceedings  United  States  Naval  Institute, 
f  United  States  Coast  and  Geodetic  Survey  Report,  1884,  Appendix  No.  6. 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


429 


latitude  and  longitude  are  then  plainly  marked,  usually  on  the  north  and  east  sides  of 
the  sheet,  at  one  extremity  of  each  parallel  and  meridian,  and  the  pencil  marks  erased. 

It  sometimes  become  necessary  to  base  topographical  work  upon  a  detached  scheme 
of  triangulation,  before  the  usual  astronomical  observations  have  been  made.  In  this 
case  the  only  elements  given  are  the  distances  from  the  points  to  two  projected  arcs  of 
rectangular  co-ordinates  (which  are  assumed)  and  the  distances  between  the  points. 
The  projection  for  plotting  these  consists  simply  of  axes  of  ordinates  and  abscissas  so 
laid  011  the  sheet  that  it  will  embrace  all  the  points  required  by  the  surveyor,  and  in  the 
manner  most  convenient  for  his  work;  and  the  points  are  plotted  from  these  by  the  inter- 
section of  two  arcs  with  the  distances  of  the  points  from  the  axes  as  radii,  either  north 
or  south,  east  or  west  of  the  axes,  as  the  plus  or  minus  sign  given  may  indicate.  The 
only  test  is  by  the  distances  between  the  points,  and  there  should  be  at  least  two  from 
each.  If  the  work  be  correctly  done,  a  regular  projection  can  be  constructed  on  the 
sheet  after  it  is  finished  and  the  required  astronomical  work  is  completed. 

In  case  it  so  happens  that  for  some  special  purpose  it  becomes  urgent  to  undertake 
a  piece  of  topography,  when  neither  the  data  for  projections  nor  co-ordinates  are  at 
hand,  plotting  by  distances  is  the  only  resource  left,  and,  of  course,  great  care  is  nec- 
essary. 

When  a  sheet  has  no  projection  it  is  advisable  to  draw  squares  of  i  ,000  or  any  speci- 
fied number  of  meters  on  it,  by  means  of  which  the  projection  can  ultimately  be  laid 
down  correctly. 

Accessories. — The  usual  accessories  for  plane-table  work  are:  Large  umbrella  for 
shading  table,  10  or  20  meter  steel  tape,  Lockes  level,  clinometer,  metal  scale,  dividers, 
pencils,  rubber,  block  of  emery  or  sand  paper,  table  of  heights,  note,  and  sketch  book. 

A  metal  chart  case  should  always  accompany  the  table  to  secure  the  sheet  from 
sudden  rain  and  other  injury  liable  to  occur  in  transportation  of  the  sheet  to  and  from 
the  field  and  for  its  safe  keeping  when  not  in  use.  Its  diameter  should  not  be  less  than 
3  inches,  for  no  sheet  can  be  rolled  to  a  less  diameter  without  serious  rupture  of  the  fiber 
of  the  paper.  It  is  also  advisable  to  have  a  rubber  cloth  for  covering  the  table  when 
it  is  carried  from  station  to  station. 

Approximate  weights. — Plane-table  movement,  18^  pounds,  boxed,  34^  pounds; 
plane-table  board,  8^  pounds,  boxed,  26^  pounds;  plane-table  alidade,  7  pounds, 
boxed,  2iJ4  pounds;  plane-table  tripod  legs,  n  pounds;  2  stadia  rods,  i6}4  pounds. 
Mountain  plane  table,  set  up  complete  with  alidade,  19^  pounds,  boxed,  36  pounds;  2 
stadia  rods,  12^  pounds. 

c.  FIELD  WORK. 

Organization  of  party. — In  organizing  a  party  for  field  work  it  is  necessary  to  have 
one  man  to  carry  the  table.  His  duty  is  to  remain  constantly  with  the  instrument, 
never  to  leave  it  unguarded;  and  while  the  topographer  is  at  work  he  holds  the  umbrella 
to  shade  the  table  from  the  sun  and  thus  protect  the  observer's  eyes  from  the  glaring 
reflections  from  the  paper  and  instruments.  "The  table  bearer  should  be  taught  at  the 
beginning  of  the  work  the  mode  of  setting  trie  table  over  a  point  and  taking  it  up  from 
the  same.  In  the  first  instance  to  grasp  firmly  the  nearest  two  legs  of  the  tripod  and 
with  the  knee  to  extend  the  third  one  until  it  reaches  the  ground  at  the  proper  distance 
from  the  point,  when  the  other  two  feet  are  set  in  position.  These  distances  from  the 


430  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

point  will  vary,  as  the  ground  may  be  level  or  sloping,  in  order  to  keep  the  tripod  head 
vertical  over  the  point  and  approximately  horizontal,  securing  the  latter  condition  by 
sighting  over  the  head  to  the  horizon.  In  taking  up  the  table  the  two  nearest  legs 
should  be  grasped  firmly  and  the  table  raised,  resting  upon  the  other  leg,  upon  which 
the  first  two  are  closed,  when  the  table  is  raised  in  place  upon  the  shoulder. 

Two  rodsmen  are  needed,  and  the  rapidity  with  which  the  work  is  executed  largely 
depends  upon  their  efficiency.  When  well  trained  they  should  be  able  to  recognize  the 
salient  points  of  the  features  to  be  mapped,  so  that  the  topographer  can  draw  in  correctly 
the  details  from  the  least  number  of  readings,  and  in  the  absence  of  an  aid  to  make  a 
sketch  of  the  intricate  portions. 

The  amount  of  assistance  an  aid  can  give  to  his  chief  is  limited  only  by  his  skill 
and  experience.  The  logical  inference  being  that  he  is  in  training  to  become  a  topog- 
rapher himself,  he  takes  charge  of  an  increasing  share  of  the  work  as  he  becomes  more 
and  more  familiar  with  the  methods  employed.  This  enables  his  chief  to  turn  his  atten- 
tion in  other  directions,  which  will  expedite  the  survey  and  increase  the  output. 

An  outline,  merely,  of  his  duties  can  be  suggested:  Building  signals,  drawing  plans 
of  intricate  details,  sketching  contours,  selecting  stations  in  advance,  running  traverse 
lines  with  auxiliary  instruments,  and  finally  in  taking  charge  of  the  plane-table  in  the 
absence  of  his  chief,  who  is  thus  afforded  the  opportunity  of  inspecting  some  difficult 
area  and  formulating  some  plan  to  meet  the  conditions  found  there. 

The  additional  number  of  men  required  to  complete  the  party  will  depend  mainly 
on  the  means  of  transportation — wagon,  horseback,  or  boat. 

Preliminary  reconnaissance. — Before  commencing  the  instrumental  work,  a  recon- 
noissance  of  the  country  should  be  made  for  the  purpose  of  recovering  triangulation 
stations  and  to  locate  signals  at  suitable  points  for  subsequent  determination  and  use. 
In  the  location  of  signals,  either  as  permanent  points  or  simply  for  temporary  forward 
lines,  a  great  deal  depends  upon  the  good  judgment  of  the  person  placing  them.  Two 
purposes  are  to  be  subserved:  first,  the  seeing  of  sufficient  known  points  to  give  a  good 
determination;  and,  second,  to  command  a  view  of  as  great  an  area  of  country,  and  as 
.many  natural  and  artificial  features  for  filling  in  the  topography,  as  possible.  It  should 
be  remarked,  also,  that  in  the  course  of  prosecution  of  the  regular  work  no  favorable 
opportunity  must  be  allowed  to  pass  for  locating  a  signal  or  determining  a  point  which 
may  at  some  future  time  be  of  service.  Advantage  should  be  taken  of  open  places  in 
the  woods  commanding  roads  or  ravines.  Piers  or  draws  of  bridges,  or  piles,  giving  lines 
up  and  down  streams,  which  have  precipitous  and  wooded  banks;  trees  of  unusual 
appearance  in  prominent  positions,  or  bearing  flags  placed  upon  them  for  the  purpose ; 
points  of  rock,  offshore  or  otherwise  ;  lightning-rods,  cupolas,  weather-cocks,  chimneys 
of  factories,  and  other  peculiar  and  marked  objects  come  within  this  category.  In  fact, 
it  may  be  set  down  as  a  rule  that  well-determined  signals  located  at  convenient  distances 
over  the  sheet  are  more  likely  to  be  too  few  than  too  frequent. 

Signal  poles  should  be  straight  and  perpendicular,  and  the  flags  upon  them  adapted 
in  color  to  the  background  against  which  they  will  be  seen  when  observed  upon. 

Graphic  triangulation. — Signals  having  been  erected  at  each  triangulation  station, 
and  also  on  all  prominent  hills  within  the  area  of  the  sheet,  where  they  would  be  useful 
in  providing  additional  control,  the  next  proceeding  will  be  to  occupy  one  of  the  former 
points. 


Coast  astU  GeodetL-  Survey  Report  1837-98    Appendix  8. 


No.  6. 


•  Chimney 


Fig.  6. 


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APPENDIX  NO.  8.     PLANK  TABLE  MANUAL. 


431 


Care  should  be  exercised  in  choosing  the  day  for  this  portion  of  the  work,  as  it  is 
essential  to  have  favorable  weather  for  a  satisfactory  test  of  the  plotted  points  in  the 
field  and  for  the  determination  of  new  ones. 

On  arrival  at  the  station  the  table  is  set  up  approximately  over  the  center  mark, 
and  the  sheet  secured  to  the  table,  so  that  it  will  be  held  firmly  and  evenly  and  not  be 
disturbed  in  its  position  by  the  friction  of  the  alidade,  nor  by  ordinary  winds.  As  the 
longest  side  of  the  board  is  usually  made  equal  to  the  width  of  the  sheet,  and  the  sheet 
is  usually  longer  than  this  width,  the  excess  of  length  is  rolled  up  inward,  turned  under- 
neath the  sides  of  the  table  and  fastened  with  a  metal  spring-clamp,  biting  from  the  top 
of  the  sheet  on  the  table  to  the  inside  of  the  roll  beneath.  One  clamp  at  each  end  of 
the  roll  serves  to  hold  the  roll-ends  securely.  The  sides  of  the  sheet  are  sometimes  held 
to  the  table  by  similar  but  shorter  clamps,  but  it  is  preferable  for  the  free  movement  of 
the  alidade,  and  more  secure  against  strong  winds,  that  a  metal  strip,  the  length  of  the 
side  between  the  end  clamps,  with  spring  clamps  fastened  to  the  outer  edge,  and  biting 
the  under  side  of  the  table,  be  used  for  holding  down  the  edges  of  the  paper. 

The  chief  and  controlling  condition  in  work  with  the  plane-table,  and  without  which 
no  accurate  work  can  be  done,  is  that  the  table  shall  be  in  position;  that  is,  that  all  lines 
joining  points  on  the  sheet  shall  be  parallel  to  the  corresponding  lines  of  nature. 

Let  T,  T',  T",  T"  (P1.6,  fig.  6),  represent  the  board  of  the  plane-table,  upon  which 
is  spread  the  sheet;  the  plotted  triangulation  point  a  upon  the  sheet  representing  the 
signal  A  upon  the  ground;  b,  the  spire  B;  c,.  the  signal  C;  and/,  the  station  P;  the 
small  letters  on  the  sheet  representing  the  centers  of  the  signals  on  the  ground,  which 
are  referred  to  by  corresponding  capital  letters. 

The  table  is  placed  approximately  level  over  the  occupied  station  P,  and  put  in 
position,  also  approximately,  by  the  eye,  so  that  the  plotted  points  on  the  sheet  are  in 
approximate  range  with  the  station  P  and  the  signals  or  objects  they  represent  in  the 
field.  Then  plumb  the  point/  over  the  station  P,  fixing  the  legs  of  the  table  firmly  in 
the  ground. 

In  maps  of  large  scale  it  is  important  to  plumb  the  plotted  point  exactly  over  the 
station,  but  on  the  usual  field  scales  of  the  Coast  and  Geodetic  Survey  (i-ioooo  arid 
1-20000)  an  approximation  with  the  eye  is  all  that  is  requisite.  To  effect  it  more 
closely  a  small  stone  is  held  underneath  the  point  and  then  dropped  to  test  the  plumb, 
or  a  plumb-bob  fastened  to  the  table  below  the  point  serves  the  same  purpose.  Plumb- 
ing arms  or  forks  are  made  and  supplied  by  the  instrument  dealers. 

The  plotted  point  having  been  plumbed  over  the  station  as  accurately  as  the  scale 
of  the  work  demands,  place  the  alidade  on  the  table  so  that  the  rule  shall  extend  across 
and  parallel  with  the  line  joining  two  of  the  leveling  screws;  loosen  the  large  clamp  screw 
tinder  the  tripod  head,  and  with  the  leveling  screws  bring  the  bubbles  of  the  two  levels 
on  the  rule  to  the  center;  clamp  the  screw  under  the  tripod  head,  and  the  table  is  level. 
Now,  unclamp  the  revolving  plate,  place  the  edge  of  the  rule  upon  the  plotted  points/ 
and  b,  the  telescope  being  directed  toward  the  spire  B,  as  shown  by  the  arrow-head  of 
the  figure,  and  revolve  the  table  until  B  is  seen  in  the  field  of  the  telescope;  clamp  the 
revolving  plate,  and  with  the  tangent  screw  of  the  movements  bisect  the  top  or  center 
of  the  spire  B  with  the  vertical  web  of  the  telescope.  The  table  \sruyxin  position,  if  the 
points  have  been  correctly  plotted  and  the  proper  objects  sighted.  To  verify  this,  place 
the  rule  upon  the  point/  again,  and  upon  the  points  a  and  c,  consecutively,  and  if  the 


432  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

two  signals  A  and  C  are  bisected  by  the  vertical  web  of  the  telescope,  the  position  is 
assured,  and  the  lines  connecting  points  of  the  sheet  are  parallel  with  the  corresponding 
lines  on  the  ground. 

The  failure  to  bisect  A  and  C  would  indicate  an  error  of  plotting  or  an  unequal 
change  of  the  dimensions  of  the  paper  (distortion),  which  must  be  examined,  and  in 
case  of  the  former  corrected,  and  in  case  of  the  latter  allowance  made  for,  as  indicated 
later  on.  (See  distortion  errors,  page  439. ) 

The  next  proceeding  is  to  draw  the  line  to  the  next  point  which  it  is  desirable  to 
occupy  or  determine,  either  some  natural  object  which  can  be  occupied,  or  a  temporary 
signal  placed  for  that  purpose,  as  the  signal  D. 

The  edge  of  the  rule  is  placed  upon  the  point  p,  and  moved  about  that  point  as  a 
center  until  the  signal  D  is  bisected  by  the  vertical  web,  and  then  a  line,  /,  is  drawn 
.along  the  edge  of  the  rule  from  p  far  enough  to  reach  the  estimated  position  on  the  sheet 
of  the  point  d,  and  at  each  end  of  the  rule  the  short  check-lines  n  n  are  drawn.  These 
check-lines  may  be  marked  on  the  sheet  with  names  of  objects,  as  in  fig.  4 — ch. ,  chim- 
ney; /.,  tree;  cup.,  cupola;  sp.,  spire;  w.  m.,  windmill;  or  numbered,  and  a  record  kept 
of  the  objects  sighted,  where  details  are  complex;  and  they  then  serve  to  reverse  the 
alidade  upon  with  the  accuracy  that  is  obtained  by  the  greatest  length  of  a  range  line. 

In  the  same  manner,  lines  to  be  afterwards  intersected  should  be  drawn  to  such 
objects  as  it  is  desired  to  determine.  This  determines  only  the  one  element  or  direction, 
it  will  be  necessary  to  determine  its  distance  from  the  point  occupied  either  by  measure 
or  by  its  intersection  by  a»  direction  from  some  other  fixed  point,  at  an  angle  not  less 
than  30°  nor  more  than  150°;  all  acute  intersections  should  be  verified  by  a  direction 
from  a  third  point. 

(Fig.  7.)  The -table  is  removed  to  the  station  A  and  placed  over  the  point,  put  in 
approximate  position,  leveled,  and  the  axis  of  revolution  clamped  as  at  station  P.  The 
rule  is  then  set  upon  the  line  a  p,  the  telescope  directed  toward  the  signal  P,  and  the 
table  put  in  position  in  the  manner  described.  Then,  keeping  the  edge  of  the  rule  upon 
a,  direct  the  telescope  to  the  signal  D  and  draw  the  line  a  d,  intersecting/,  and  deter- 
mining the  position  of  the  point  d  upon  the  sheet,  corresponding  to  D,  and  bearing  the 
same  relation  in  directions  and  distances  from  the  points  p,  a,  6,  and  c  as  the  signal  D 
does  from  P,  A,  B,  and  C.  All  lines  to  other  objects  which  were  drawn  from  p,  and 
which  objects  can  be  seen  from  A,  are  intersected  and  determined  in  the  same  manner. 

When  a  direction  has  been  drawn  from  a  station  to  any  undetermined  point  that 
may  be  occupied,  the  position  of  the  point  may  be  determined  by  occupying  it  with  the 
table,  and  putting  the  table  in  position  by  the  line  drawn  to  it,  and  resecting  Upon  a  signal 
whose  corresponding  point  is  plotted  upon  the  sheet. 

(Fig.  8.)  The  table  is  placed  over  the  point  D,  put  in  approximate  position,  leveled, 
etc.,  as  at  the  previous  stations.  The  edge  of  the  rule  is  then  placed  upon  the  line  dp, 
passing  through  the  point/,  so  that  the  checks  n  n  are  just  visible  along  the  edge,  and 
the  telescope  directed  toward  the  signal  P,  and  the  table  put  in  position.  The  rule  is 
then  placed  with  its  edge  bisecting  one  of  the  plotted  points,  such  as  b,  which  will  give 
a  good  intersection  (the  nearer  90°  the  better)  with  the  line/",  and  is  moved  about  that 
point  as  a  center  until  the  spire  B  is  bisected  by  the  vertical  web.  A  line  is  now  drawn 
along  the  edge  of  the  rule  accurately  through  b,  crossing  the  line  f.  If  this  line  inter- 


Coast  and  Geodetic  Survey  Report  1897-38   Appendix  8. 


No.  7. 


Fig.  9 


Fig.15. 


Fig.  19. 


Fig.16. 


CoasL  and  Geinietu   .Si/./  ivi  Itffiurt  lti!i~?  !)0    AfifjeJiiiuc  ft. 


No.8. 


Class 


Indeterminate 


Ind 


Class  3 


Fig.  10. 


Coast  and  Geodetic  Survey  Report  2tM7-M   ApperuLi.?  8. 


Fig.  13 


Fig.  12. 


I 


I 


n 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  433 

sects  the  liney"at  the  point  d,  the  position  of  the  latter  is  assured,  and  a  delicate  hole 
with  the  dividers  should  be  pricked  at  the  point,  surrounded  by  a  small  circle  in  pencil. 

Resection  upon  any  other  determined  point  will  verify  its  position. 

From  this  point,  d,  directions  are  observed  and  drawn  to  verify  the  previous  inter- 
sections upon  chimney,  tree,  cupola,  windmill,  etc. 

There  are  occasions  on  occupying  some  station  that  several  objects  are  seen  whose 
position  it  is  desirable  to  determine  by  prosection,  but  there  is  doubt  of  their  being 
recognized  from  other  stations.  A  new  station  is  then  occupied  close  by  the  first  one 
and  new  lines  drawn  to  the  objects.  The  intersection  thus  obtained  will  necessarily  be 
acute,  but  will  materially  assist  in  their  identification  from  other  localities. 

All  lines  should  be  drawn  lightly  and  carefully  close  to  the  edge  of  the  rule  with 
a  finely-sharpened  hard  pencil.  If  the  table  and  alidade  be  in  proper  condition,  the 
contact  of  the  edge  of  the  rule  with  the  paper  will  be  perfect  throughout  its  length, 
and  in  drawing  a  line  along  the  edge  care  must  be  taken  to  preserve  the  same  inclination 
of  the  pencil  and  to  keep  it  sharp.  If  the  rule  should  be  raised  from  the  paper  at  any 
part,  great  care  is  to  be  observed  that  the  pencil  does  not  run  under  the  edge  and  thus 
deviate  from  a  straight  line. 

Amount  of  control. — There  is  no  fixed  ratio  between  the  number  of  determined 
points  and  the  number  of  square  miles  of  the  region  to  be  surveyed  or  square  inches  of 
plane-table  sheet. 

The  greater  the  number  of  points  well  distributed  over  the  latter  the  less  likelihood 
of  error  or  annoyance  due  to  the  distortion  of  the  paper  in  the  future. 

A  large  number  also  makes  it  easy  for  the  topographer  to  determine  by  resection 
subordinate  stations  for  mapping  the  details,  and  in  consequence  fewer  traverse  lines 
need  be  run. 

More  than  sufficient  for  these  purposes  are  not  necessary,  and  it  is  important  when 
carrying  on  a  graphic  triangulation  not  to  waste  valuable  "time  and  favorable  weather, 
but  to  advance  this  part  of  the  work  as  rapidly  as  possible  before  the  sheet  becomes 
affected  by  exposure. 

The  three-point  problem. — A  subordinate  station  is  located  at  any  desired  place 
where  a  good  view  of  the  surrounding  features  can  be  obtained.  If  this  place  has  not 
been  previously  determined  it  is  now  effected  by  means  of  the  resection  of  lines  from 
three  fixed  points. 

The  special  advantages  of  the  plane  table  as  a  mapping  instrument  are  due  to  the 
rapidity  with  which  it  obtains  results  by  the  method  of  graphic  triangulation  and  to 
the  facility  it  affords  the  topographer  in  determining  his  position  at  an  unknown  point 
by  the  graphic  solution  of  the  three-point  problem. 

When  the  latter  method  is  applicable;  that  is,  when  the  country  is  open  and  signals 
easily  seen,  its  superiority  over  a  system  of  traverse  lines  is  manifest.  The  topog- 
rapher then  is  at  liberty  to  choose  his  ground  without  reference  to  his  last  station  or  to 
one  succeeding.  He  is  not  tied  down  to  a  backsight  nor  restricted  by  the  conditions 
imposed  by  a  foresight.  He  need  not  set  up  his  instrument  on  an  area  barren  of  detail 
nor  cut  his  way  through  obstacles  (bushes,  hedges,  trees)  to  establish  a  station  at  a 
commanding  point  of  view. 
S.  Doc.  48 28 


434  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

The  number  and  situation  of  the  stations  is  governed  solely  by  the  amount  and 
location  of  the  information  to  be  mapped.  On  the  other  hand,  traverse  stations  are 
chosen  on  account  of  their  visibility,  and  many  of  them  are  of  no  service  whatever 
beyond  carrying  the  line  forward. 

•  Definitions. — When  the  table  is  imperfectly  oriented,  the  lines  drawn  from  the  three 
projected  points  will  not  intersect  at  one  point,  except  when  all  four  are  on  the  circum- 
ference of  a  circle.  (See  fig.  10,  positions  marked  indeterminate.)  Except  in  this  case, 
two  of  the  lines  will  be  parallel,  intersected  by  a  third  (see  case  5,  station  on  range  line 
between  two  fixed  points,  and  case  6,  station  on  prolongation  of  range  line),  or  they 
will  form  a  small  triangle  called  the  triangle  of  error.  (See  shaded  triangles,  fig.  10. ) 

The  triangle  formed  by  the  three  fixed  points  is  called  the  great  triangle  (Fig.  10 
ABC),  and  the  circle  passing  through  the  same  points  the  great  circle. 

There  are  a  number  of  graphic  solutions  of  the  three-point  problem,  but  all  save 
three  are  better  suited  to  the  drafting  room,  with  its  appliances,  than  to  the  conditions 
which  exist  in  the  field. 

Lehmann's  method*  of  solution  is  the  simplest,  most  direct,  and  applies  under  all 
circumstances.  It  is  based  on  a  fact  which  can  be  stated  in  the  form  of  a  rule. 

Rule  i. — The  true  point  is  always  distant  from  the  three  lines  drawn  from  the  three 
fixed  points,  in  proportion  to  the  distances  of  the  latter  from  the  point  occupied. 

Demonstration. — A,  B,  C  (PI.  7,  fig.  9)  are  the  projections  of  the  three  signals  from 
which  it  is  desired  to  determine  by  resection  the  position  of  a  fourth  point,  D.  The 
table  being  out  of  position  to  the  right,  the  triangle  of  error  formed  by  the  three  lines 
from  A,  B,  and  C  is  ab,  ac,  be.  The  true  point  occupied  lies  at  D,  being  at  the  intersec- 
tion of  the  circles  AB  ab,  AC  ac,  BC  be.  Now,  if  perpendiculars  be  drawn  from  D  to 
the  lines  drawn  from  A,  B,  and  C,  we  shall  have — 

Da  :  Db  :  :  DA   :  DB  or  Db  :  DC  ;  :  DB  :  DC. 

It  is  convenient  to  make  the  following  classification,  based  upon  the  locality  of  the  true 
point  in  relation  to  the  three  fixed  points: 

Class  i. — When  the  point  sought  falls  within  the  great  triangle  (fig.  10,  case  i ) ,  PI.  8. 

Class  2. — When  the  point  sought' falls  within  either  of  the  segments  of  the  great 
circle  formed  by  the  sides  of  the  great  triangle  as  chords.  (Case  2.) 

This  also  includes  case  3  where  the  three  fixed  points  (B,  C,  D)  are  in  a  straight 
line,  in  which  case  the  points  are  considered  as  being  in  the  circumference  of  a  circle  of 
infinite  diameter,  and  the  point  sought  always  lying  in  one  of  the  segments  of  the  great 
circle. 

Class  j.- — When  the  point  sought  falls  without  the  great  circle  (Case  4). 

Since  it  is  not  always  easy  to  quickly  decide  where  the  true  point  should  be  located 
in  reference  to  the  triangle  of  error  according  to  rule  i ,  three  additional  rules  are  given 
to  serve  as  guides.  The  surveyor  is  assumed  to  be  facing  the  signals  and  the  directions 
tight  and  left  are  given  accordingly. 

Rule  2. — The  point  sought  is  always  to  be  found  on  the  same  side  of  each  line  draxvn 
from  the  three  fixed  points:  that  is,  if  it  is  on  the  right  side  of  one  line  it  is  on  the  right 
side  of  each  of  the  other  two;  if  on  the  left  of  one,  it  is  on  the  left  of  the  other  two. 

*See  United  States  Coast  and  Geodetic  Report,  1880,  App.  13,  for  additional  methods  of  solution. 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


435 


Ride  j. — When  the  point  sought  falls  within  either  of  the  three  segments  of  the 
great  circle  formed  by  the  sides  of  the  great  triangle,  the  line  drawn  from  the  middle 
point  lies  between  the  true  point  and  the  intersection  of  the  other  two  lines  (fig.  10, 
class  2), 

Rule  4.. — When  the  point  sought  is  without  the  great  circle  it  is  always  on  the  same 
side  of  the  line  from  the  most  distant  point  as  the  point  of  intersection  of  the  other  two 
lines  (fig.  10,  class  i). 

The  point  sought  in  cases  of  class  i  must  fall  within  the  triangle  of  error.  No 
other  position  would  satisfy  the  conditions  of  rule  2. 

Its  definite  position  is  then  decided  upon  according  to  rule  i,  by  estimating  its 
proportional  distance  from  each  line. 

Rules  3  and  4  are  complementary  to  rule  2  and  are  especially  useful  in  classes  2  and  3. 

Procedure. — In  practice,  the  position  of  the  point  sought  is  first  determined  with 
reference  to  one  line  by  either  rule  3  or  4;  it  then  follows  from  rule  2  that  it  must  be  on 
the  corresponding  side  of  the  other  two  lines.  Rule  i  is  then  applied. 

Example,  Class  2,  Case  2. — The  line  drawn  from  A,  the  middle  point,  is  to  the 
right  of  the  intersection  of  the  lines  from  B  and  C,  therefore  (rule  3)  the  point  sought 
must  be  on  its  right,  and  also  (rule  2),  to  the  right  of  the  line  from  B  and  C. 

Example,  Class  j,  Case  f. — The  intersection  of  the  lines  from  B  and  C  fall  to  the 
right  of  the  line  from  A,  the  farthest  point;  therefore  (rule 4)  the  point  sought  must  be 
on  its  right,  and  also  (rule  2)  on  the  right  of  the  line  from  B  and  from  C. 

There  are  two  cases,  5  and  6,  where  no  triangle  of  error  is  formed,  two  of  the  lines 
drawn  from  fixed  points  being  parallel,  intersected  by  a  third.  In  practice  the  topog- 
rapher would  recognize  at  once  that  he  was  either  on  a  range  between  two  points  or  on 
the  prolongation  of  a  range  line,  and  orienting  by  it  there  would  be  no  deflection  of  the 
table,  and  consequently  the  lines  would  all  intersect  at  one  point.  The  examples  are, 
however,  instructive,  since  they  indicate  the  treatment  in  cases  of  points  which  fall  near 
a  range.  * 

Case  5. — When  the  point  sought  is  on  or  near  the  range  between  two  fixed  points 
the  true  point  must  be  between  the  parallel  lines  to  satisfy  the  conditions  of  rule  2.  Its 
position  with  reference  to  the  intersecting  line  follows  from  the  same  rule.  In  the 
figure  the  point  sought  being  between  the  lines  from  B  and  C,  is  to  the  right  of  each; 
therefore  it  is  to  the  right  of  the  line  from  A. 

Case  6. — When  the  point  sought  is  on  or  near  the  prolongation  of  a  range  hjie  the 
true  point  will  be  outside  the  parallel  lines  and  011  the  side  of  the  line  to^lie  ^^rest 
fixed  point  of  the  range.  If  the  point  sought  were  placed  on  the  othei^srere,  it  would 
be  impossible  to  satisfy  the  conditions  of  rule  i .  In  the  figure  it  will  be  seen  that  the 
point  sought  must  be  outside  the  lines  from  A  and  B  to  satisfy  rule  2 ,  and  to  their  rigfit 
to  satisfy  rule  i ,  and  also  to  the  right  of  the  line  from  C. 

The  preceding  cases  are  all  examples  of  the  conditions  which  may  occur  when  the 
table  is  deflected  to  the  right.  By  turning  the  printed  side  of  the  illustration  to  the 
light  and  looking  at  the  figure  through  the  paper,  it  will  appear  reversed  and  the  ' '  cases ' ' 
will  then  be  examples  of  conditions  which  may  occur  when  the  table  is  deflected  to 
the  left. 

Repetition. — When  the  true  point  has  been  estimated  and  marked  on  the  sheet  in 
accordance  with  the  foregoing  rules,  a  new  orientation  is  made.  If  the  lines  from  the 


436  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

three  stations  now  intersect  at  that  point  it  proves  the  estimate  to  have  been  correct 
and  the  position  is  determined.  If  a  new  triangle  of  error  is  formed,  it  indicates  a 
faulty  estimate,  and  the  operation  must  be  repeated. 

Orienting  by  estimation. — A  small  triangle  of  error  is  the  result  of  a  close  orienta- 
tion, which  the  topographer  endeavors  to  accomplish  at  the  first  trial  by  taking  advan- 
tage of  any  range  that  may  exist  either  of  signals  or  other  details  already  platted  on 
the  sheet.  It  will  serve  the  same  purpose  if  they  are  near  enough  in  line  to  estimate  a 
direction  on  the  sheet  to  the  farthest  object,  and  then  to  orient  by  it. 

The  declinatoire  may  be  used,  but  it  is  a  slow  and  inaccurate  method  of  orientation. 

It  is  employed  for  this  purpose  by  placing  the  straight  edge  of  the  box  containing 
the  needle  upon  a  magnetic  meridian,  previously  traced  upon  the  map,  and  revolving 
the  table  until  the  needle  points  to  o°*  or  north,  on  the  graduated  arc  at  the  end  of  the 
box.  The  magnetic  meridian  is  roughly  determined  at  any  \vell-determined  station, 
when  the  table  is  properly  oriented  by  the  use  of  the  declinatoire  itself,  the  meridian 
line  being  drawn  upon  the  sheet  along  the  straight  edge  of  the  box  when  the  needle 
points  to  o°.  Or  the  table  may  be  oriented  by  making  the  straight  edge  of  the  box 
coincide  with  one  of  the  meridians  of  the  projection  nnd  then  turning  the  board  until 
the  needle  points  to  the  right  or  left  of  the  zero,  according  to  the  amount  and  direction 
of  the  njagnetic  deviation. 

Bcssef  s  method  by  inscribed  quadrilateral  is  the  simplest  method  by  construction. 
The  objection  to  it  arises  from  .the  fact  that  in  practice  the  intersection  of  the 
construction  lines  often  falls  beyond  the  limit  of  the  board. 

By  this  method  a  quadrilateral  is  constructed  with  all  the  angles  in  the  circumfer- 
ence of  a  circle,  one  diagonal  of  which  passes  through  the  middle  one  of  the  three  fixed 
points  and  the  point  sought.  On  this  line  the  alidade  is  set,  the  telescope  directed  to 
the  middle  point,  and  the  table  is  in  position.  Resection  upon  the  extreme  points 
intersects  in  this  line  and  determines  the  position  of  the  point  sought. 

PI.  9.  (Figs,  n,  12,  13,  and  14.)  L,et  a  b  c  be  the  points  on  the  sheet  represent- 
ing the  signals  A  B  C  on  the  ground.  The  table  is  set  up  at  the  point  to  be  deter- 
mined (d)  and  leveled.  The  alidade  is  set  upon  the  line  ca,  and  a  directed,  by 
revolving  the  table  to  its  corresponding  signal  A,  and  the  table  clamped;  then,  with 
the  alidade  centering  on  c,  the  middle  signal  B  is  sighted  with  the  telescope  and  the 
line  ce  drawn  along  the  edge  of  the  rule.  The  alidade  is  then  set  upon  the  line  ac  and 
the  Jalescope  directed  to  the  signal  C,  by  revolving  the  table,  and  the  table  clamped. 
ThS^  wiAthe  alidade  centering  on  a,  the  telescope  is  directed  to  the  middle  signal  B, 
and  the  lmefc<?  is  drawn  along  the  edge  of  the  rule.  The  point  e  (the  intersection  of 
these  two  lines)  will  be  in  the  line  passing  through  the  middle  point  and  the  point 
sought.  Set  the  alidade  upon  the  line  be,  direct  b  to  the  signal  B  by  revolving  the 
table,  and  the  table  will  be  in  position.  Clamp  the  table,  center  the  alidade  upon  #, 
direct  the  telescope  to  the  signal  A,  and  draw  along  the  rule  the  line  ad.  This  will 
intersect  the  line  be  at  the  point  sought.  Resection  upon  C,  centering  the  alidade  on  c 
in  the  same  manner  as  upon  A,  will  verify  its  position. 

The  opposite  angles  of  the  quadrilateral  adce  being  supplementary, 

Z.ace  and  £ade  are  subtended  by  the  same  chord  ae,  and  /_cae  and  Z.cde  are  sub- 
tended by  the  same  chord  ce;  consequently,  the  intersection  of  ae  and  ce  at  e  must  fall 
on  the  line  db;-  or,  the  segments  of  two  intersecting  chords  in  a  circle  being  reciprocally 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  437 

proportional,  the  triangles  adf  and  cef  are  similar,  and  the  triangles  cdf  and  aef  are 
similar,  and  d,  f,  and  e  must  be  in  a  right  line  passing  through  b. 

In  using  this  method  the  triangle  formed  by  the  three  fixed  points  can  be  contracted 
or  extended,  as  may  be  desirable,  by  drawing  a  line  parallel  to  the  one  joining  the  two 
extreme  points,  and  terminated  by  those  joining  the  extremes  with  the  middle  point. 
The  graphic  solution  can  then  proceed  in  the  same  manner  as  that  described  for  an  orig- 
inal triangle. 

Tracing-cloth  protractor.  — The  third  method  consists  in  laying  off  the  angles  between 
the  three  known  points  on  tracing  cloth  or  paper,  and  using  this  as  a  protractor,  deter- 
mine the  position  of  the  unknown  point. 

Fasten  a  sheet  of  tracing  cloth  or  paper  to  the  board,  marking  upon  it  a  point  to 
represent  the  unknown  point.  Draw  through  it  lines  toward  the  three  known  points. 
Then  shift  the  tracing  cloth  over  the  sheet  until  each  of  the  three  lines  passes  through 
the  plotted  point  corresponding  to  the  point  toward  which  it  is  drawn.  The  position  of 
the  unknown  point  will  be  at  the  intersection  of  these  lines. 

This  method  is  less  exact  and  not  so  convenient  as  the  other  two  previously  described, 
and  is  impracticable  in  any  wind. 

TWO-POINT    PROBLEM. 

The  ocQasion  may  arise  where  it  is  desirable  to  place  the  table  in  position  at  a  given 
point,  from  which  only  two  determined  points  are  visible.  This  may  be  done  by  the 
following  methods: 

The  first  mode  possesses  the  virtue  of  making  no  linear  measurement,  and  demon- 
strates in  a  very  satisfactory  manner  the  effectiveness  of  the  table  in  determining  posi- 
tion by  resection. 

(Plate  7,  figs.  5,  6,  7,  and  8.) — Two  points,  A  and  B,  not  conveniently  accessible, 
being  given,  by  their  projections  a  and  b,  to  put  the  plane-table  in  position  at  a  third 
point,  C.  (The  capital  letters  refer  to  points  on  the  ground,  and  the  small  ones  to  their 
corresponding  projections.) 

Select  a  fourth  point,  D,  so  that  the  intersections  from  C  and  D  upon  A  and  B 
make  sufficiently  large  angles  for  good  determinations.  Put  the  table  approximately  in 
position  at  D,  by  estimation  or  by  compass,  and  draw  the  lines  Aa  ~Bd,  intersecting  in 
d;  through  d  draw  a  line  directed  to  C.  Then  set  up  at  C,  and  assuming  the  point  c  on 
the  line  dC,  at  an  estimated  distance  from  d,  and  putting  the  table  in  a  position  parallel 
to  that  which  is  occupied  at  D,  by  means  of  the  line  cd,  draw  the  lines  from  c  to  A1  and 
from  c  to  B.  These  will  intersect  the  lines  dA  dE  at  points  a'  and  b' ,  which  form  with 
c  and  d  a  quadrilateral  similar  to  the  true  one,  but  erroneous  in  size  and  position. 

The  angles  which  the  lines  ab  and  a'b'  make  with  each  other  is  the  error  in  posi- 
tion. By  constructing  now  through  c  a  line  cd'  making  the  same  angle  with  cd  as  that 
which  ab  makes  with  a'b' ,  and  directing  this  line  cd'  to  D,  the  table  will  be  brought  into 
position,  and  the  true  point  c  can  be  found  by  the  intersections  of  a  A  and  &B. 

Instead  of  transferring  the  angle  of  error  by  construction,  we  may  conveniently  pro- 
ceed as  follows,  observing  that  the  angle  which  the  line  a'b'  makes  with  ab  is  the  error 
in  the  position  of  the  table.  As  the  table  now  stands,  a'b'  is  parallel  with  AB,  but  we 
want  to  turn  it  so  that  ab  shall  be  parallel  to  the  same,  if  we,  therefore,  place  the  alidade 
on  a'b'  and  set  up  a  mark  in  that  direction,  then  place  the  alidade  on  ab  and  turn  the 


438  COAST  AND  GEODETIC  SURVEY  REPORT,  1897^8. 

table  until  it  again  points  to  the  mark,  then  ab  will  be  parallel  to  AB,  and  the  table  is 
in  position. 

Another  method  is  as  follows  (Fig.  9): 

Two  points,  A  and  B,  not  conveniently  accessible,  being  given  by  their  projections 
a  and  b,  to  put  the  plane-table  in  position  at  a  third  (undetermined)  point,  C. 

Set  up  the  table  at  the  point  sought  as  nearly  in  position  as  can  be  done  with  the 
eye,  and  resect  upon  A  and  B,  intersecting  the  line  be  at  c' .  The  angle  ac'b  is  the  true 
angle  at  the  point  occupied,  subtended  by  AB,  being  the  angle  of  nature  actually  drawn; 
therefore,  the  true  point  must  be  on  the  circumference  of  the  circle  passing  through  abc' . 
Construct  this  circle.  Measure  off  a  base,  CD,  at  least  half  the  length  of  CB,  at  right 
angles,  or  nearly  so,  to  be,  in  either  direction  most  convenient.  Set  up  a  signal  at  D, 
and  with  the  alidade  draw  the  line  cfd.  Remove  the  table  to  D,  and,  by  means  of  a 
signal  at  C  (the  point  sought),  and  the  line  dc' ,  bring  the  table  into  a  position  parallel 
to  that  which  it  occupied  at  C.  With  the  alidade  centering  on  d,  observe  the  signal  B, 
and  draw  the  line  dU  intersecting  cb  at  b' .  c'b'  is  the  distance  of  the  point  C  from  B, 
and  this  distance  laid  off  on  the  circle  ac'b  as  a  chord  from  b  will  give  c",  the  true  posi- 
tion of  the  point  C.  A  fourth  point  may  then  be  occupied,  and  by  resection  upon  A, 
B,  and  C  the  accuracy  of  the  determination  of  C  verified. 

Where  it  is  possible  to  get  the  two  signals  A  and  B  in  range,  it  is  easy  to  determine 
the  position  of  a  third  point  by  a  mode  long  practiced  by  topographers. 

Set  up  the  table  anywhere  on  the  range  line,  and  orient  by  the  latter.  Resect  on 
the  unknown  point  drawing  the  line  anywhere  on  the  sheet  most  convenient.  Leave  a 
signal  at  the  occupied  point  on  the  range  line  and  set  up  the  instrument  at  the  unknown 
point.  Orient  by  the  line  drawn  when  at  the  station  on  the  range  line,  sighting  on  the 
latter  station.  The  table  will  now  be  in  a  parallel  position  to  that  when  on  the  range 
line,  which  is  the  true  position,  and  the  unknown  point  may  be  determined  by  resec- 
tion upon  the  two  fixed  points  and  their  projections. 

Deflection  of  long  lines. — In  adjusting  lines  of  intersection  upon  a  point  or  object 
from  a  series  of  stations,  when  these  lines  do  not  coincide  in  one  point,  as  they  are 
usually  derived  from  signals  at  unequal  distances,  the  error  should  not  be  divided  equally 
among  them,  but  in  proportion  to  their  lengths  if  the  discrepancies  are  not  eliminated 
by  the  rules  for  distortion  errors  given  later. 

It  should  be  borne  in  mind  that  very  short  lines  from  a  determined  point — as,  for 
instance,  to  the  corners  of  a  fenced  road,  where  the  table  occupies  the  center  of  the 
intersection  of  two  roads — may  be  taken  with  no  apparent  error  when  the  table  is  deflected 
to  some  extent  from  its  true  azimuth,  but  that  in  this  case  a  prolonged  line  will  be  con- 
siderably out  at  its  further  extremity. 

A  long  line  should  never  be  obtained  by  the  prolongation  of  a  short  one  from  a  back 
station  where  there  is  no  small  check  line,  or  some  other  point  in  that  prolongation 
already  fixed. 

It  will  be  apparent  that  the  more  nearly  at  right  angles  intersecting  lines  cross  each 
other,  the  more  clearly  the  point  will  be  defined;  acute  intersections,  as  far  as  possible, 
should  be  avoided,  and,  even  when  they  are  crossed  by  a  third  line  at  a  satisfactory 
angle,  a  fourth  line,  or  an  accurate  rod  reading  from  a  well-determined  point,  is  advis- 
able if  within  reach. 

Sometimes  a  position  is  established  by  measuring  along  the  estimated  direction 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


439 


from  a  nearly  fixed  point  and  then  orienting  by  this  assumed  position  and  a  distant 
point.  This  method  should  be  used  with  caution,  but  is  generally  reliable  for  rodding 
the  detail  in  the  vicinity. 

Distortion  errors* — The  distortion  of  a  plane  table  sheet  destroys  the  perfect  pro- 
portions which  exist  between  the  fixed  points  and  their  plotted  representatives  on  the 
sheet. 

The  diagram,  PI.  10,  illustrates  the  effect  distortion  would  have  in  the  determina- 
tion of  a  point. 

No.  10 


G  F 

A,  B,  C,  etc.,  are  plotted  in  their  true  relations.  After  the  sheet  has  contracted 
a,  b,  c,  etc.,  represent  the  relations  those  points  have  assumed.  The  paper  contracts 
at  a  uniform  but  different  rate  in  each  direction. 

The  plane  table  is  supposed  to  be  at  x,  the  exact  center  of  the  figure,  and  it  is 
required  to  determine  the  position  by  the  distorted  points  a,  b,  c,  etc.  By  reversing  the 
telescope,  we  immediately  ascertain  that  we  are  directly  on  the  line  HD.  Reversal 
will  also  show  that  we  are  on  the  lines  AE,  CG,  and  BF.  But  the  distortion  is  not 
apparent  until  the  telescope  is  pointed  at  the  signals,  and  the  lines  are  drawn  011  the 
sheet.  Then  if  we  orient  by  the  line  HD,  we  shall  produce  the  figure  of  the  diagram, 
giving  five  determinations,  i,  2,  3,  4,  and  x,  each  made  with  four  well-conditioned 
points.  Any  one  of  these  conditions  would  be  considered  satisfactory  if  we  had  not  the 
other  points  to  show  that  something  was  wrong.  To  orient  by  the  line  BF  will  produce 
the  same  result.  But  if  we  take  the  diagonal  AE,  we  shall  have  two  positions  at  5  and 
7,  formed  by  the  intersection  of  the  diagonal  points,  with  the  lines  from  the  other  points 


*See  Distortion  of  Plane  Table  Sheets,  Ogden,  Science,  Vol.  XI,  No.  270. 


440  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

running  wild.  Using  the  diagonal  CG  would  give  two  points  at  6  and  8,  with  the  lines 
from  the  other  points  running  wild  as  before. 

Position  by  compromise. — There  is  no  question  that  out  of  the  nine  positions  devel- 
oped by  these  settings,  that  at  A^is  the  only  true  compromise.  When  the  sheet  is  dis- 
torted, all  positions  are  compromises;  and  X  is  the  true  compromise  in  this  case,  for  it 
is  on  the  lines  CG,  AE,  etc. :  a  below  and  e  above,  the  line  connecting  A  and  E,  by 
equal  quantities.  A  line  drawn  through  the  distorted  points  a  and  e  must  pass  through 
the  middle  point  X.  The  positions  5,  6,  7,  and  8  can  not  be  true  because  lines  forming 
them  will  not  pass  through  the  opposite  points  when  extended,  which  we  know  to  be 
the  condition  that  must  be  filled. 

Rules: 

(1)  A  station  made  with  three  points  that  are  on  the  lines  of  contraction,  the 
resecting  lines  forming  nearly  right  angles  at  their  intersection,  will  give  the  true  posi- 
tion in  relation  to  all  points  in  the  sheet  (as  h,  b,  d}. 

(2)  A  similar  condition  of  right-angular  intersection  at  the  station,  but  the  lines 
forming  diagonals  to  the  lines  of  contraction,  will  give  the  worst  possible  position  for 
the  station  (as  a,  c,  and  e*). 

(3)  A  station  made  with  three  points  on  one  of  the  lines  of  contraction  will  give 
the  correct  orientation  of  the  table  (a,  /i,  and  c)  but  not  the  correct  position. 

(4)  In  estimating  errors  of  the  point  due  to  distortion,  those  situated  on  the  lines 
of  contraction  require  110  allowance,  however  distant. 

Application. — If  the  change  in  the  sheet  due  to  contraction  or  expansion  gives  the 
same  percentage  of  the  units  of  length,  both  lengthwise  and  transverse  of  the  sheet,  the 
points  are  still  in  their  true  relative  position,  and  the  projection  is  practically  as  good 
as  when  laid  on  the  paper,  but  is  on  a  slightly  altered  scale.  When  the  percentage 
of  change  in  the  units  of  length  is  greater  in  one  direction  than  the  other  the  sheet  and 
projection  are  distorted;  and  to  make  a  station  by  the  three-point  problem  the  change 
of  scale  in  each  direction  must  be  allowed  for.  The  difficulty  in  making  such  allow- 
ances is  not  great  if  the  principal  effects  of  distortion  in  the  sheet  are  borne  in  mind.  It 
would  not  be  permissible,  even  were  it  practicable,  to  make  new  points  on  the  sheet,  as 
this  would  destroy  the  geographic  position.  It  is  necessary,  therefore,  to  assume  the 
new  points  by  estimation,  applying  the  percentage  of  change  to  the  distances  measured 
between  the  points  on  the  lines  of  change — that  is,  on  lines  parallel  to  the  edges  of  the 
sheet.  If  the  point  occupied  and  the  point  sighted  to  are  on  a  line  parallel,  or  nearly 
so,  to  one  edge  of  the  sheet,  its  movement  from  the  distortion  can  only  be  along  that 
line.  When  the  position  of  the  point  sighted  to  is  found  situated  to  one  side  of  the  line 
parallel  to  the  edge  of  the  sheet,  the  distortion  will  also  affect  it  in  the  direction  at  right 
angles  to  that  edge,  and  the  effect  of  the  distortion  will  be  most  apparent  when  the 
angle  of  deflection  is  45°  and  the  position  at  as  great  a  distance  from  the  point  occupied 
as  the  paper  will  permit.  As  the  angle  of  deflection  increases  above  45°  the  effect 
becomes  less  and  disappears  at  90°,  when  the  position  will  fall  again  in  a  line  parallel 
to  an  edge  of  the  sheet. 

Referring  to  the  diagram,  PI.  10,  to  make  a  station  with  the  three  points  a,  b,  c: 
If  the  sheet  \vere  not  distorted  the  station  would  be  at  X;  A ,  B,  and  C  being  the  true 
positions  plotted  when  the  projection  was  drawn.  But  the  sheet  having  contracted,  a, 
b,  and  c  show  the  relative  positions  of  these  points;  therefore  we  make  such  allowance 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


441 


for  the  contraction  derived  from  measuring  the  unit  of  length  that  we  can  place  or 
imagine  a  and  c  to  be  where  the)'  belong,  at  A  and  C.  b  requifes  no  change,  as  it  is  on 
a  line  parallel  to  the  edge  of  the  sheet.  To  locate  A  we  must  know  the  distances 
(approximately)  h  to  a  and  h  to  X,  which  multiplied  by  the  percentages  of  contraction 
(in  this  case)  will  give  the  distance  of  A  above  and  to  the  left  of  a.  The  same  process 
locates  C. 

If  the  station  were  to  be  made  with  the  points  a,  c,  and  e,  all  three  points  would 
have  to  be  imagined  in  a  new  position  by  the  same  process  that  A  has  been  located. 

Stations  made  in  this  way  will  be  good  for  all  local  sketching  within  an  area  that  the 
contraction  of  the  sheet  is  inappreciable  ;  but  to  take  cuts  on  distant  objects  from  such 
a  station  the  orientation  of  the  table  must  be  changed.  If  an  object  is  somewhere  near 
the  direction  of  a  and  the  table  at  the  compromise  station  X,  the  table  must  be  oriented 
by  a  and  X,  the  imaginary  position  A  being  discarded. 

The  same  processes  apply  to  all  positions  on  the  sheet  for  the  station  occupied. 

Height  of  instrument. — Having  obtained  the  horizontal  position  on  the  sheet  of  the 
occupied  point,  the  next  proceeding  in  the  logical  sequence  is  the  determination  of  the 
height  of  the  instrument  above  some  datum  plane,  in  order  to  locate  and  draw  the  con- 
tours of  the  area  surrounding  the  station.  The  angle  read  and  the  distance  between  the 
occupied  point  and  the  observed  point  measured  from  the  map,  the  height  is  computed 
by  means  of  the  following  table,  in  which  correction  is  made  for  curvation  and  refraction. 

Table  showing  the  height  in  feet  corresponding  to  a  given  angle  of  elevation  and  a  given 

distance  in  meters. 


Meters. 

300 

400 

500 

6OO 

700 

800 

900 

I,  OOO 

I,  IOO 

I,  200 

1,300 

1,400 

1,500 

i,  600 

1,700 

i,  800 

1,900 

^,000 

Angle. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feel. 

Feet. 

Feet 

Feel. 

% 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

i' 

°'3 

0-4 

0-6 

0-6 

0-8 

0-9 

I'O 

I'2 

i  '3 

i'5 

17 

1-8 

2'0 

2'2 

2-3 

2'5 

27 

2'8 

2 

0-6 

o'S 

I'D 

I  '2 

i  '5 

17 

i  "9 

2'I 

2'4 

2'6 

2-9 

3'i 

3  "4 

37 

3'9 

4'2 

4-5 

47 

3 

0-9 

fa 

1-5 

1-8 

2'2 

2'5 

2-8 

3'i 

3'4 

3'8 

4-2 

4'4 

4-8 

5'3 

5'6 

5  "9 

6'3 

6-6 

4 

ra 

i  o 

2'0 

2-4 

2-8 

3'2 

3-6 

4'* 

4'5 

4  "9 

5  '4 

5'8 

6'3 

16-8 

7-2 

7-6- 

8'i 

8-6 

5 

i'5 

i  '9 

2'4 

2'9 

3  "5 

4-0 

4'5 

5'° 

5'5 

6-1 

6-6 

7'i 

77 

8'3 

8-8 

9'4 

9'9 

10-5 

6 

i  -8 

2'3 

2'9 

3'5 

4-2 

4-8 

S'JI 

5  '9 

6-6 

7-2 

7  '9 

8'5 

9'i 

9-8 

io'4 

ii'i 

117 

12-4 

7 

2'I 

27 

3'4 

4'i 

4'8 

5'5 

6-2 

6-9 

7-6 

8-4 

9'i 

9-8 

io'6 

11-4 

I2'I 

12-8 

13  "5 

I4'3 

8 

2'4 

3'i 

3'9 

4-6 

5'5 

6-3 

7'i 

7'9 

87 

9'5 

10-4 

iri 

I2'O 

12-9 

137 

H'5 

I5'3 

16-2 

9 

27 

3'5 

4'4 

5'2 

6-2 

7-0 

7  '9 

8-8 

97 

107 

n-6 

I2'5 

I3'4 

14-4 

15  "3 

16-2 

17-2 

18-1 

10 

2-9 

3'8 

4  '9 

5'8 

6-8 

7-8 

8-8 

9-8 

lo'S 

n-8 

I2'8 

13-8 

14-9 

'5'9 

i6'9 

17-9 

ig'o 

20'O 

II 

3'2 

4-2 

5'3 

6-4 

7  '5 

8-6 

9-6 

107 

n-8 

13-0 

14  i 

15-1 

16-3 

I7'5 

18-6 

197 

20'8 

21  '9 

12 

3'5 

4-6 

5'8 

6-9 

8-2 

9'3 

io'5 

117 

12-9 

14-1 

I5'3 

i6'5 

177 

19*0 

20'2 

21-4 

22-6 

23-8 

13 

3-8 

5'° 

6-3 

7-5 

8-8 

IO'I 

11-4 

12-6 

I3'9 

I5'2 

16-6 

17-8 

19*2 

20-5 

21-8 

23'  I 

24-4 

257 

H 

4'i 

5'4 

6-8 

8-1 

9'5 

io~9 

I2'2 

I3/6 

i5-o 

16-4 

17-8 

19-1 

20-6 

22  '0 

23-4 

24-8 

26-2 

27  "6 

15 

4  "4 

5'7 

-•2 

8-6 

I0'2 

n-6 

13  '» 

I4'5 

i6'o 

I7'5 

ig'o 

20-5 

22'0 

23-6 

25-0 

26-5 

28'0 

29'5 

16 

47 

6'i 

77 

9-2 

o-S 

12-4 

13  '9 

i5'5 

17-1 

187 

20-3 

21-8 

23  '5 

25-I 

267 

28-2 

29-9 

3i  '4 

17 

4'9 

6-5 

8-2 

Q-8 

i  '5 

13"! 

14-8 

'6'5 

18-1 

19-8 

2i'5 

23-1 

24-9 

26-6 

28-3 

30-0 

317 

33  "4 

iS 

5-2 

6-9 

8-7 

io-4 

2'2 

13  "9 

157 

i7'4 

19-2 

21  "O 

22-8 

24  "5 

26-3 

23'2 

29-9 

317 

33  '5 

35'3 

J9 

5'5 

7'3 

9'i 

10.9 

2-8 

M7 

i6'5 

18-4 

20'2 

22'I 

24-0 

25-8 

-77 

297 

3i'5 

33'4 

35'3 

37'2 

20 

77 

9-6 

"'5 

3  '5 

:5'4 

i/'4 

21'3 

23  "3 

25-2 

27-2 

2y'2 

3I-2 

33'2 

35'  i 

37"i 

39'  i 

21 

6'i 

IO'I 

\2'\ 

14-2 

16-2 

IV  J 

20-3 

22'3 

24H 

26-5 

28-5 

30-6 

327 

34'8 

36-8 

38-9 

41  'o 

22 

6-4 

8-4 

io'6 

I2'6 

I4'9 

T7'o 

19-1 

21'2 

23  '4 

25  "5 

277 

29-8 

32-0 

34'3 

36-4 

38-5 

407 

42-9 

23 

6'7 

8-8 

in 

IJ-a 

I.VS 

177 

2O'O 

22'2 

24-4 

267 

29'O 

3  1  '2 

33'S 

35*8 

38-0 

40  '3 

42'5 

44-8 

24 

6-9 

9-2 

1  1  '5 

16-2 

18-5 

23-I 

25'5 

30-2 

32-5 

34  '9 

37  '3 

39  '6 

42-0 

44'3 

467  " 

25 

fa 

.  9-6 

I2'O 

14  '4 

i6'9 

I9'3 

-•r; 

24-1 

26-5 

29*0 

3*"4 

33-8 

360 

4''3 

437 

46-2 

48-6 

1 

442 


COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 


Table  showing  the  height  in  feet  corresponding  to  a  given  angle  of  elevation  and  a  given 
*      distance  in  meters — Continued. 


Meters. 

300 

400 

500 

600 

700 

800 

900 

1,000 

I,  IOO 

I,  200 

1,300 

1,400 

1,500 

i,  600 

i,  700 

i,  800 

1,900 

2,000 

Angle. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

26' 

7'5 

9'9 

i2'5 

14-9 

173 

2O"O 

22-5 

25-0 

27-6 

30-1 

327 

35'2 

37  '8 

40-4 

42-9 

45  '4 

48*0 

5<J5 

27 

7'S 

10-3 

13-0 

I5'5 

18-2 

20'8 

23-4 

26-0 

28-6 

3i  '3 

33  '9 

36-5 

39'2 

41-9 

44  '5 

47'J 

49-8 

52-4 

28 

8-1 

107 

I3'4 

16-1 

18-9 

21  '5 

24-2 

26-9 

29-7 

32-4 

35'2 

37-8 

40-6 

43  '4 

46-1 

48-8 

51-6 

54  '3 

29 

8-4 

ii'i 

I3'9 

167 

I9'5 

22-3 

25'i 

27-9 

3°7 

33-6 

36  '4 

39'2 

42-1 

45  '° 

47-8 

•  50-6 

53  "4 

56-2 

3° 

87 

n'5 

14-4 

17-2 

20'2 

23-1 

26  'o 

28-9 

31-8 

347 

37'6 

40-5 

43'5 

46-5 

49'4 

52-3 

55  "2 

58-2 

40 

"'5 

I5'3 

19-2 

22-9 

26-9 

307 

34  '6 

38-4 

42-3 

46-1 

50-0 

53  '9 

52'8 

61-7 

65-6 

69-4 

73  '3 

77'3 

5° 

14-4 

19-1 

23  "9 

28-7 

33  '5 

38-3 

43'2 

47'9 

527 

57'6 

62-4 

67-2 

72-1 

77  -o 

81-8 

86-6 

91  '5 

96-3 

1°00 

17-2 

22  '9 

287 

34  '4 

40-2 

46-0 

517 

57  '5 

63-3 

69*0 

74-8 

80-6 

86-4 

92'3 

98-0 

104 

no 

U5 

I   JO 

20'I 

267 

33  '5 

40-1 

46-9 

53'6 

60-3 

67-0 

73'8 

80-5 

87-2 

93  '9 

100-7 

i°7'5 

1  14  '3 

121 

128 

134 

i  20 

23  'o 

3°'5 

38-3 

45'8 

53'6 

6l'2 

6g'o 

76-6 

84-2 

91-9 

99  -6 

107-3 

115-1 

123 

131 

138 

146 

154 

i  30 

25-8 

34  '4 

43"° 

5i-6 

60-3 

69-0 

777 

86-1 

947 

103-4 

II2'O 

1207 

130 

138 

H7 

155 

164 

173 

i  40 

287 

38-2 

47-8 

57'3 

66-9 

76-6 

86-3 

95'6 

105-2 

U5 

124 

134 

144 

153 

163 

173. 

182 

192 

i  5° 

3I-6 

42'O 

52-6 

63-0 

73'6 

84-2 

94'9 

105-2 

H57 

126 

137 

147 

158 

169 

179 

190 

200 

211 

2  OO 

34  '4 

45'8 

57'4 

68-9 

80 

92 

103 

"5 

126 

138 

149 

161 

172 

184 

195 

207 

218 

230 

2  30 

43'° 

57  '3 

71-7 

86-0 

IOO 

"5 

129 

144 

158 

172 

186 

20  1 

215 

230 

244 

259 

273 

287 

3  oo 

5i-6 

68-8 

86-2 

103-2 

1  20 

138 

155 

172 

190 

207 

224 

241 

259 

276 

293 

3IO 

328 

345 

3  30 

6o'2 

80-4 

100-5 

120-5 

141 

161 

181 

201 

221 

241 

261 

281 

302 

322 

342 

362 

382 

402 

4  oo 

68-9 

91-8 

114-8 

1377 

161 

184 

207 

230 

253 

276 

299 

322 

345 

368 

391 

414 

437 

460 

Example  of  use  of  table  of  heights. 
[Angle  of  elevation  from  point  A  to  point  B,  distant  from  each  other  i  756  meters=  i°  56/.] 


50'. 

50' 

50'. 

06'. 

06'. 

06'. 


Meters.  Feet. 

I    700    179-00 

50* 5'26 

6    '63 

i   700   10-40 

50   -29 

6   -04 


195-62 

Point  B  is  195 '62  feet  above  point  A. 

Formula  for  determining  heights  by  a  vertical  angle  and  distance. — The  difference  of 
level  consists  of  two  parts,  that  which  arises  from  the  angle  of  elevation  above  the 
horizontal  plane  of  the  station  and  that  which  is  due  to  the  curvature  of  the  earth. 
The  former  depends  upon  the  angle  and  distance,  the  latter  upon  the  distance  and  the 
earth's  radius.  If  a'  be  the  angle  of  elevation  in  minutes  of  arc,  d  the  distance,  h  the 
height,  then,  as  the  tangent  of  i'  is  3413t,  we  have  for  the  first  part  h=^^a'd,  if  h 
and  d  are  both  expressed  in  the  same  units  of  length,  but  if  d  is  expressed  in  meters  and 
h  in  feet,  one  meter  being  3*28  feet,  we  get  h—  ,  0148«V.  For  the  fraction  1T^  we  may 
conveniently  and  with  sufficient  accuracy  put  1 0\  s  less  210  of  1 010  ff,  and  thus  find  the 
rule:  Multiply  the  distance  in  meters  with  the  member  of  minutes  of  arc,  point  off  the 
thousandth  part,  and  subtract  the  twentieth  part  of  the  number  thus  obtained.  This  will 
give  the  first  portion  of  difference  of  height,  whether  elevation  or  depression. 

The  second  term,  depending  on  the  curvature,  varies  as  the  square  of  the  distance, 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  443 

and  amounts  to  0*22  foot  in  i  ooo  meters,  including  the  effect  of  ordinary  refraction. 
As  with  the  instruments  under  consideration  extreme  accuracy  is  not  attainable,  it  is  plain 
that  for  distances  under  i  ooo  meters  this  term  may  be  neglected.  When  the  distance 
is  greater,  we  have  the  following  rule:  Take  the  thousandth  part  of  the  distance  in  meters, 
square  the  same,  having  regard  to  the  first  decimal  figure,  and  multiply  by  o'22.  This 
term  is  always  positive.  If  the  first  term  be  an  elevation,  it  is  increased;  if  a  depression, 
it  is  diminished  by  the  second  term. 

Example. — Distance  =  5  500  meters;  angle  of  elevation,  36'. 


ToW«  =     5'5 

subtract  ^g  9'9  square       =  30^2 

multiply  by  0*22 
first  term          1 8S  •  i 
second  term         5  "6  second  term  6^64 


194-7  =  difference  of  elevation  in  feet. 


444 


COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

TABLE  II.—  Table  showing  the  height,  in  meters,  corre- 

( Curvature  and  refraction 


ICO 

20O 

300 

400 

500 

600 

700 

Soo 

900 

10OO 

1100 

1200 

0°       I' 

0-03 

o-o6 

0-09 

0-13 

O'i6 

O'2O 

0-24 

0-28 

0-32 

0-36 

0-40 

o-45 

2 

o-o6 

O'I2 

o-iS 

0-24 

0-31 

0-37 

0-44 

0-5I 

0-58 

0-65 

0-72 

o'79 

3 

0-09 

0-18 

0-27 

0-36 

o-45 

0-55 

0'64 

0-74 

0-84 

0-94 

1-04 

1-14 

4 

0'12 

0-24 

0-36 

0-48 

o-6o 

072 

0-85 

097 

I'lO 

1-23 

1-36 

i"39 

5 

0-15 

0-29 

o-44 

o-59 

0-74 

O-qO 

T05 

1*21 

1-36 

1-52 

r  -68 

1-84 

o°     6' 

0-18 

o'35 

o-53 

0-70 

0-89 

1-07 

1-26 

1-44 

1-62 

rSi 

2-00 

2-19 

7 

O'2O 

0-41 

0'62 

0-82 

1-04 

1-24 

1-46 

I-67 

1-89 

2'10 

2-32 

2'44 

8 

0-23 

0-47 

0-70 

0-94 

1-18 

I-42 

r66 

j'go 

2-16 

2-39 

2-64 

9 

0'26 

o-53 

079 

i'o6 

i  -33 

I  '59 

1-87 

2-14 

2-41 

2-68 

2-96 

3-24 

10 

0-29 

0-58 

0-88 

ri8 

i-47 

1-77 

2-07 

2-37 

2-68 

2-98 

3-28 

3'59 

0°    II" 

0-32 

0-64 

0-97 

1-29 

1-62 

I-94 

2-27 

2  '6O 

2]93 

3-27 

3-60 

3'74 

12 

0-35 

•70 

1-05 

1-41 

176 

2'12 

2-48 

2'84 

3-56 

3-92 

4  '29 

13 

0-38 

076 

1-14 

1-52 

1-91 

2-29 

2-68 

3^7 

3-46 

3-85 

4-24 

4*63 

H 

0-41 

0-82 

1-23 

1-64 

2-05 

2'47 

2-88 

3'3° 

3-72 

4-14 

4'98 

15 

0-44 

0-88 

1-32 

1-76 

2  '2O 

2-64 

3-o8 

4-88 

5'33 

o°   1  6' 

o*47 

o-93 

1-40 

1-87 

2-34 

2-82 

3-29 

3'77 

4-24 

4-72 

5-20 

5'68 

17 

0-50 

o-99 

1-49 

1-99 

2-49 

2-99 

3'49 

3-90 

4-50 

5-01 

5'52 

6-03 

18 

0-52 

1-05 

1-58 

2'10 

2'64 

3-I7 

3-70 

477 

5-30 

5*84 

6-38 

19 

o-55 

i-ii 

1-66 

2'22 

2-78 

3'34 

3-90 

4-46 

6-16 

6-63 

20 

0-58 

1-17 

i-75 

2-34 

2-93 

3-51 

4-11 

4-70 

5-29 

5-88 

6-48 

7-08 

0°    2I/ 

o'6i 

•23 

1-84 

2-45 

3^7 

3-69 

4-3i 

4'93 

5-55 

6-17 

6-80 

7'43 

22 

0*64 

•28 

i-93 

2-57 

3"22 

3-86 

4-51 

5-16 

5-8: 

6-47 

7-12 

23 

0-67 

'34 

2-01 

2-69 

3-36 

4-04 

4-72 

5-40 

6-08 

6-76 

7'44 

8-12 

24 

070 

•40 

2-10 

2-80 

3-50 

4-21 

4-92 

5-63 

6'34 

7-05 

8-47 

25 

o-73 

-46 

2'ig 

2-92 

3^5 

4-39 

5-12 

5-88 

6-60 

7-34 

8-08 

8-82 

0°    26/ 

0-76 

"52 

2-28 

3^4 

3-80 

4-56 

5-33 

6  '09 

6-86 

7;63 

8-40 

9-17 

27 

o'79 

'     "57 

2-36 

3'i5 

3'95 

4'74 

5-53 

6-33 

7-12 

8-72 

9-52 

28 

0-82 

•63 

2-45 

3-27 

4-09 

4-91 

5'74 

6-56 

7-38 

8'2I 

9-04 

9-87 

29 

0-84 

.69 

2'54 

3-38 

4'24 

5-08 

5-94 

6"79 

7-65 

8-50 

9-36 

IO'22 

3° 

0-87 

i'75 

2-62 

3-50 

4-38 

5-26 

6-14 

7'O2 

7-91 

8-79 

9-68 

IQ'57 

o°  40' 

1-16 

2'33 

3-50 

4'66 

5-84 

7-00 

8-1.8 

9-35 

10-53 

11-70 

12-88 

I4-06 

50 

i'45 

2-91 

4^7 

5-83 

7-29 

8-75 

IO'22 

n-68 

13-14 

I4'62 

16-08 

I7-55 

I       00 

i-75 

3'49 

5-24 

6-99 

8-74 

10-50 

12-25 

14-01 

I5-76 

17-52 

19-28 

21-04 

I       10 

2-04 

4-08 

6-12 

8-16 

IO'2O 

1  2  '24 

I4'29 

i6'33 

18-38 

20-43 

22-48 

24-53 

I       20 

2-33 

4-66 

6-99 

9-32 

u-66 

13-99 

I6'33 

18-66 

21-00 

23-34 

25-68 

28-03 

1°    30' 

2-62 

5-24 

7-86 

10-48 

13-11 

I5-73 

I8'36 

20'  99 

23*62 

26-25 

28-88 

3I-52 

I       40 

2-91 

5-82 

874 

11-65 

14-56 

17-48 

20'4O 

23-32 

26-24 

29-16 

32-09 

35-01 

I       50 

3'20 

6-40 

9-61 

12-82 

1  6  -02 

19-23 

22-44 

25-65 

28-86 

32-08 

35*29 

38-5I 

2      OO 

3'49 

6-99 

10-48 

13-98 

17-49 

20-98 

24^8 

27-98 

3I-48 

34-99 

42-00 

2°    30' 

4'37 

8-74 

13-11 

17-28 

21-85 

26-22 

30'60 

34-97 

39*35 

43'73 

48-11 

52-49 

3    oo 

5-24 

io'48 

I5-73 

20-97 

26'22 

31*47 

36-72 

41-97 

47*22 

57-73 

62-99 

3    30 
4    oo 

6-12 
6-99 

12-24 
13-99 

18-36 
20-98 

24-48 
27-98 

30'6o 

41'98 

42-85 
48-98 

44-97 
55-9S 

62-99 

61-23 
69-99 

67-36 
77-00 

73-49 
84-01 

i 

100 

200 

300 

400 

500 

600 

700 

800 

900 

IOOO 

1100 

I20O 

APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 
spending  to  given  angles  of  elevation  and  distances  in  meters. 
takeii  into  account. ) 


445 


1300 

1400 

1500 

1600 

1700 

1800 

1900 

2OOO 

2IOO 

2200 

2300 

2400 

2500 

0-49 

o-54 

o"59 

0-64 

0-69 

0-74 

0-80 

0-85 

0*90 

0*96 

I  '02 

i  -08 

1-14 

0°        I' 

0-87 

o'95 

I  -02 

no 

1-18 

1-26 

1-35 

i-43 

I-52 

1*60 

1-69 

1-78 

1-87 

2 

I  '25 

i'35 

I'46 

i'57 

1-68 

1-79 

1-90 

2-01 

2-I3 

•  2-24 

2-36 

2-48 

2  '60 

3 

1-63 

176 

1-90 

2-03 

2-17 

2-31 

2-45 

2'59        2'74 

2-88 

3-03 

3'i8 

3-33 

4 

2*OO 

2-17 

2-33 

2-50 

2-67 

2-83 

3-00 

3-l8 

3'35 

3-52 

3-70 

3-88 

4-05 

5 

2-38 

2'57 

2-77 

2-96     3-16 

3'35 

3-56 

3-76 

3^ 

4-16 

4-37 

4-57 

4-78 

o°     6' 

276 

2-98 

3-20 

3'43 

3-66 

3-88 

4-11 

4-34 

4-57 

4-80 

5^4 

5-27 

5-5I 

if 

S-M 

3  '39 

3-64 

3-89 

4-I5 

4-50 

4-66 

4-92 

5'I8 

5'44 

5-70 

5-97        6-24 

8 

3'52 

3-8o 

4-08 

4-36 

4-64 

4'93 

5-22 

5-50 

5'79 

6-08 

6-37 

6-67 

6-96 

9 

3-90 

4-20 

4-5i 

4-82 

5-14 

5-45 

5^-77 

6-08 

6-40 

6-72 

7-04 

7-36 

7-69 

10 

4-27 

4-61 

4'95 

5-29 

5-63 

5-98 

6-32 

6-67 

7-01 

7-36 

7-71 

8-06 

8-42 

0°     II' 

4-65 

5-02 

5-39 

5-76 

6-13 

6-50 

6-87 

7-25 

7-62 

8-00 

8-38 

8-76 

9-I4 

12 

5  "03 

5  '42 

5-82 

6-22 

6-62 

7-02 

7-43 

7-83 

8-24 

8-64 

9-05 

9-46 

9-87 

13 

5  "4i 

5-83 

6-26 

6-69 

7-12 

7-55 

7-98 

8-41 

8-85 

9-28 

9-72 

10-16 

io-6o 

14 

578 

6-24 

6-70 

7-I5 

7-62 

8-07 

8-53 

8-99 

9-46 

9-92 

10-39 

10-86 

11-32          15 

6-16 

6-65 

yi3 

7-62 

8-ii 

8-59 

9-08 

9-58 

10-07 

10-56 

1  1  -06 

n'55 

12-05    °°   1  6' 

6-54 

7  '05 

7-56 

8-08 

8-60 

9-12 

9-64 

10-16 

10-68 

1  1  -20 

Ji'73 

12*25 

12-78       17 

6-92 

7-46 

8-00 

8-55 

9-09 

9-64 

10-19 

10-74 

11*29 

11-84 

12-40 

12*95 

13-51           18 

7-30 

7-87 

8-44 

9"oi 

9-59 

10-16 

10-74 

11-32 

11-90 

12-48 

13-06 

13-65 

14*23          19 

7-68 

8-28 

8-88 

9-48 

io-oS 

10*69 

11-30 

11-90 

12-51 

13-12 

*3'73 

I4-35 

14-96              20 

8-05 

8-68 

9-3i 

9'94 

10-58 

II'2I 

11-85 

12-48 

13-12 

13-76 

14-40 

15-04 

15*69     0°    2I/ 

8-43 

9-09 

9'75 

10-41 

11-07 

11-74 

12*40 

13-07 

I3-73 

14-40 

15-07 

I5-74 

16-42              22 

8*81 

9-50    10-19    io'S8 

n'57 

12-26 

12-95 

13-65 

H'34 

15-04 

I5-74 

.-  16*44 

'7T4              23 

9-19 

9-90 

10-62 

H'34 

I2'O6 

12-78 

13-51 

14-23 

14-96 

15-68 

16*41 

17*14 

17-87,             24 

9-57 

10-31 

1  1  -06 

11-81 

12-56 

13-31 

14-06 

14-81 

I5-57 

16*32 

.   17*08 

17*84 

1  8  '60          25 

9'94 

10-72 

11-50 

12-27 

13-05 

13-83 

14-61 

I5-39 

16-18 

16*96 

I7-75 

iS'54 

19-32    o°  26' 

10-32 

11-13 

n'93 

12-74 

13-55 

14-35 

15-16 

15-98 

16*79 

17-60 

18*42 

19-23 

20-05          27 

1070    11-53 

12-37 

13-20 

14-04 

14-88 

15-72 

16-56 

17*40 

18-24 

19*09 

I9-93 

20-78          28 

1  1  -08    1  1  -94 

12-80 

13-67 

14-53 

15-40 

16-27 

17-14 

18*01 

18-88 

19*76 

20-63 

21-51          29 

11-46 

12-35 

13-24 

I4-I3 

15-03 

15-92 

16-82 

17-72 

18*62 

19-52 

20*42 

21-33 

22-23 

3° 

I5'24 

16-42 

17-60 

18-79 

19-97 

2I'l6 

22-35 

23*54 

2473 

25-82 

27*12 

28*31 

29-50   o°  40' 

19-02 

20-49 

21-97 

23-44 

24-92 

26-40 

27-88 

29-36 

30-84 

32-32 

33-8i 

35-29 

36-7S 

50 

22-81 

24-57 

26-33 

28-10 

29-87 

31-64 

33'4i 

35-i8 

36-95 

38-72 

40*50 

42-28 

44-06 

I       OO 

26-59 

28-64 

30-70 

32-75 

34-81 

36-87 

38-94 

41-00 

43-06 

45-I3 

47-I9 

49*26 

5I-33 

I        IO 

30-37 

32-72 

35-o6 

37-41 

39-76 

42-10 

44-46 

46-82 

49-I7 

5  1  '53 

53-89 

56-25 

58-61 

I      20 

34-i6 

3679 

39-43 

42-07 

44-71 

47-35 

49'99 

52-64 

55-28 

57-93 

60*58 

63-23 

65-88 

i°  30' 

37'94 

40-87 

43-80    46-73 

49-66 

52-59 

55-52    58-46 

61-40 

64-34 

67*28 

70*22 

73"i6 

I      40 

41-72    44-94 

48-16    51-38 

54-61 

57-83 

6ro6    64-28 

67-51 

70-74 

73-97 

77'2i 

80*44 

i     50 

45-50    49-02 

52-53 

56-04 

59-56 

63-07 

66-59 

70-10 

73-63 

77T5 

80*67 

84-20 

87-72 

2       00 

56-87    61-26 

65-64 

70-03 

74-42 

78-81 

83-20 

87-59 

91-98 

96-38 

100*78 

105*17 

109*57 

2°    30' 

68-24    73'5i 

78-76    84-02 

89-29 

94-55 

99-82  105-10 

no'35 

115-62 

120*89 

126*16 

I3I-44 

3     oo 

79-63    85-76 

91-89    98-03 

104-18  110-31,116-45  122-59  I28'74   134-88 

141-03 

147-18 

I53-33 

3     30 

91-02 

98-03 

105-04 

II2'06 

117-07  126-09 

133-10 

140-12 

147*14 

154*18 

161-19 

168-21 

175-24 

4     oo 

1300 

1400 

1500 

1600 

1700 

1800 

I90O 

2OOO 

2IOO 

22OO 

2300 

2400 

2500 

446 


COAST  AND  GEODETIC  SURVEY  REPORT,   i897~c 


PI.  32  is  a  diagram  showing  the  method  of  constructing  a  scale  for  taking  off  the 
heights  corresponding  to  a  given  angle  and  distance. 

Table  of  factors  for  computing  differences  in  elevation* 

To  obtain  the  difference  in  elevation  in  feet  multiply  the  horizontal  distance  in  meters  by  the 
factor  in  this  table  corresponding  to  the  observed  angle  of  elevation  or  depression.  The  factors  are 
given  for  each  ten  minutes,  but  the  value  for  the  nearest  minute  may  be  interpolated,  using  the  column 
of  differences  for  one  minute.  The  result  is  still  to  be  corrected  where  necessary  for  the  effect  of 
curvature  and  refraction. 

TABLE  III. 


Angle. 

o' 

10' 

20' 

3°' 

40' 

5°' 

60' 

Differ- 
ence for 
i  minute 
(fourth 
decimal 
place). 

o 

O 

o-oooo 

0-0095 

0*0191 

O*O286 

0*0382 

0*0477 

0-0573 

9'5 

I 

0-0573 

0-0668 

0-0764 

0*0859 

0-0955 

0*1050 

0*1146 

9*6 

2 

0-1146 

0-1241 

0*1337 

0*1432 

0-I528 

0*1624 

0*1719 

9*6 

3 

0-1719 

0-1815 

o'igii 

0-2007 

O'2IO2 

0*2198 

0*2294 

9*6 

4 

0-2294 

0-2390 

0*2486 

0-2582 

0-2678 

0-2774 

0*2870 

9*6 

5 

0-2870 

0-2967 

0-3063 

0-3I59 

0-3255 

0-3352 

0-3448 

9-6 

6 

0-3448 

0-3545 

0*3641 

0-3738 

0-3835 

0*3932 

0*4028 

9'7 

7 

0-4028 

0-4125 

0*4222 

0-43I9 

0-4416 

0-45I4 

0*4611 

9'7 

8 

0-4611 

0-4708 

0*4806 

0*4903 

O-5OOI 

0*5098 

0*5196 

9*8 

9 

0-5196 

0-5294 

0-5392 

0*5490 

0-5588 

0*5687 

0-5785 

9-8 

10 

0-5785 

0-5884 

0*5982 

0-6081 

0-6179 

0-6278 

0-6377 

9'9 

ii 

0-6377 

0-6476 

0*6576 

0-6675 

0-6774 

0-6874 

0*6974 

9'9 

12 

0-6974  1 

0-7073 

0*7173 

0-7273 

0-7374 

0-7474 

0-7574 

10*0 

13 

0-7574 

.  0-7675 

0*7776 

0-7877 

0*7978 

0-8079 

0*8180 

10*1 

14 

0-8180 

0-8282 

0-8383 

0-8485 

0*8587 

0-8689 

0*8791 

IO*2 

15 

0-8791 

0-8893 

0*8996 

0-9099 

O*92OI 

0-9304 

0*9408 

10*3 

16 

0*9408 

0-9511 

0-9615 

0-9718 

0*9822 

0*9926 

1*0031 

10*4 

17 

1-0031 

I  '0135 

i  '0240 

1-0344 

1*0449 

1-0555 

1*0660 

10*5 

18 

i'o66o 

I  -0766 

i  '0872 

i  -0978 

I*I084 

I'ligo 

1*1297 

10*6 

19 

1-1297 

1*1404 

1*1511 

I*i6i3 

I*I726 

I-I833 

1*1941 

10-7 

20 

1-1941 

1-2050 

1*2158 

1-2266 

1-2375 

1*2485 

1-2594 

10*9 

21 

i  '2594 

1-2704 

1*2813 

1-2924 

.  I-3034 

I-3I44 

1-3255 

11*0 

22 

I-3255 

1-3367 

1-3478 

I-3590 

1*3702 

1*3814 

1-3926 

11*2 

23 

1-3926 

1-4039 

1*4152 

1-4266 

i  "4379 

1-4493 

1*4607 

11*4 

24 

1-4607 

1*4722 

1*4836 

I-4952 

1*5067 

I-5I83 

1*5299 

n'5 

25 

1-5299 

1-5415 

.  I-5532 

1-5649 

1*5766 

1*5884 

1*6002 

11*7 

26 

i  -6002 

1*6120 

1*6239 

1-6358 

1*6477 

1-6597 

1*6717 

11*9 

27 

1-6717 

1*6837 

1-6958 

1*7079 

1-7200 

1*7322 

1*7444 

12*1 

28 

1-7444 

17567 

1-7690 

1*7814 

I-7937 

I  '806  1 

i  -8186 

12*4 

29 

1-8186 

1*8311 

1*8436 

1*8562 

1*8688 

1*8815 

i  "8942 

12*6 

30 

i  "8942 

1*9069 

1*9197 

1*9326 

1-9454 

I-9584 

I-97I3 

12-9 

31 

I-97I3 

1-9843 

1-9974 

2*0105 

2-0236 

2*0368 

2-0501 

!3"i 

32 

2-0501 

2-0634 

2-0767 

2*0901 

2-1036 

2*1171 

2*1306 

13-4 

33 

2-1306 

2*1442 

2*1578 

2*1715 

2-1853 

2*1991 

2*2130 

137 

34 

2*2130 

2-2269 

2*2408 

2-2548 

2-2689 

2*2831 

2*2973 

14*0 

35 

2-2973 

2-3115 

2-3258 

2-3402 

2-3546 

2*3691 

2-3837 

14*4 

36 

2-3837 

2-3983 

2*4130 

2-4277 

2-4425 

2-4574 

2-4723 

14*8 

37 

2-4723 

2-4873 

2*5023 

2-5I75 

2-5327 

2-5479 

2-5633 

15*2 

38 

2-5633 

2-5787 

2-5942 

2-6097 

2-6253 

2*6410 

2*6568 

15-6 

39 

2-6568 

2*6726 

2*6885 

2-7045 

2*7206 

2-7367 

2-7530 

16*0 

40 

2-7530 

2*7692 

2*7856 

2  '802  1 

2-8186 

2-8353 

2*8520 

16*5 

4i 

2-8520 

2*8688 

2*8857 

2-9026 

2*9197 

2*9368 

2-954I 

17*0 

42 

2-954I 

2*9714 

2-9888 

3-0063 

3-0239 

3*0416 

3-0594 

17*6 

43 

3  '0594 

3-0773 

3-0953 

3-H34 

3-1316 

3-I499 

3-1683 

18*1 

44 

3-1683 

3*1868 

3  '2054 

3-224I 

3-2429 

3*26l8 

3*2808 

18*8 

*  Furnished  by  G.  R.  Putnam,  Assistant,  Coast  and  Geodetic  Survey. 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


Table  of  corrections  for  curvature  and  refraction* 


447 


The  correction  in  feet  for  the  combined  effect  of  curvature  and  refraction  is  given  for  each  100 
meters'  distance,  the  thousands  of  meters  being  given  in  the  column  to  the  left  and  the  hundreds  in 
the  upper  line.  The  correction  is  to  be  added  to  the  difference  of  elevation  for  angles  of  elevation 
and  subtracted  for  angles  of  depression,  or  it  is  always  to  be  added  to  the  uncorrected  elevation  of  the 
point  to  be  determined  from  point  of  observation. 

Example:  At  a  station  whose  elevation  is  i  ooo  feet  (at  telescope),  angle  to  signal  =  3°  elevation, 
horizontal  distance  =  5  ooo  meters.  From  Table  III  factor  is  0-1719,  which  multiplied  by  5  ooo  =  859*5 
feet.  From  Table  IV  correction  is  5-5  feet.  Corrected  difference  of  elevation  =  859-5 -f  5-5  =  865 
feet,  which  added  to  i  ooo  =  i  865  feet  for  elevation  of  signal.  If  the  above  angle  to  signal  be  3° 
depression,  then  corrected  difference  of  elevation  =  859-5  —  5-5  =  854-0  feet,  which  makes  height  of 
signal  =  i  ooo  —  854-0  =  146-0  feet. 

TABLE  IV. 


Distance  in 
meters. 

o 

100 

200 

300 

400 

500 

600 

700 

800 

900 

I  OOO 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

Feet. 

o 

O'O 

O'O 

O'O 

O'O 

O'O 

O'l 

O'l 

O'l 

O'l 

0'2 

O"2 

I    000 

0'2 

0-3 

0'3 

0'4 

0-4 

0'5 

0-6 

0-6 

0-7 

0-8 

0-9 

2   OOO 

0-9 

1.0 

n 

I'2 

I  '3 

1-4 

l'5 

1-6 

17 

1-9 

2'0 

3  °°° 

2'0 

2'I 

2'3 

2'4 

2-6 

27 

2-9 

3'o 

3'2 

3'4 

3'5 

4  ooo 

3-5 

37 

3'9 

4'I 

4'3 

4'5 

47 

4'9 

5'i 

5*3 

5  '5 

5  ooo 

5'5 

5'8 

6-0 

6-2 

6'5 

67 

7-0 

7-2 

7'4 

77 

8-0 

6  ooo 

8-0 

8-2 

8-5 

8-8 

9-1 

9  "4 

97 

I0'0 

IO'2 

io-6 

10-9 

7  ooo 

10-9 

II'2 

n'5 

n-8 

I2'I 

12-5 

12-8 

13*1 

13*5 

13-8 

14-2 

8  ooo 

14-2 

i4'5 

14-9 

15*3 

15-6 

i6x> 

16-4 

16-8 

I7-2 

17-6 

18-0 

9  ooo 

18-0 

18-4 

iS'8 

19-2 

19-6 

20'0 

20-4 

20-8 

21-3 

21-7 

22'2 

10  ooo 

22'2 

22'6 

23-0 

23-5 

24-0 

24-4 

24-9 

25-4 

25-8 

26-3 

26-8 

II    OOO 

26-8 

27'3 

27-8 

28-3 

28-8 

29'3 

29-8 

30-3 

30-8 

3i-4 

3^9 

12    OOO 

3*'9 

32-4 

33'o 

33  "5 

34'  i 

34'6 

35  '2 

•357 

36-3 

36-9 

37'4 

13  ooo 

37'4 

38-0 

38-6 

39'2 

39-8 

40-4 

41  "o 

41-6 

42-2 

42-8 

43  '4 

14  ooo 

43'4 

44-1 

447 

45  '3 

46-0 

46-6 

47-2 

47'9 

48-5 

49-2 

49'8 

15  ooo 

49-8 

50-5 

5i-2 

5i-9 

52-5 

53'2 

53  "9 

54'6 

55'3 

56-0 

567 

16  ooo 

567 

57'4 

58-2 

58-9 

59'6 

60-3 

6i'o 

6r8 

62-5 

63  '3 

64-0 

17  ooo 

64-0 

64-8 

65-6 

66-3 

67-1 

67-9 

68-6 

69-4 

70-2 

71*0 

71-8 

18  ooo 

71-8 

72-6 

73  '4 

74-2 

75'o 

75-8 

76-7 

77'5 

78-3 

79-1 

80-0 

19  ooo 

80-0 

80-8 

817 

82-5 

,83-4 

84-2 

85-1 

86-0 

86'9 

877 

88-6 

*  Furnished  by  G.  R.  Putnam,  Assistant,  Coast  and  Geodetic  Survey. 


448 


COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 
Table  of  factors  for  computing  differences  in  elevation. 


To  obtain  the  difference  in  elevation  in  meters  multiply  the  horizontal  distance  in  meters  by  the 
factor  in^  this  table  corresponding  to  the  observed  angle  of  elevation  or  depression.  The  factors  are 
given  for  each  ten  minutes,  but  the  value  of  the  nearest  minute  may  be  interpolated,  using  the  column 
of  differences  for  one  minute.  The  result  is  still  to  be  corrected  where  necessary  for  the  effect  of 
curvature  and  refraction. 

TABLE  V. 


Angle 

o' 

lo' 

20' 

3o' 

4<y 

5°' 

60' 

Difference 
for  i  min- 
ute (4th  dec. 
place) 

0 

O 

O'OOOO 

O'OO29 

0-0058 

0x3087 

o'on6 

0-0145 

0-0175 

2-9 

I 

•0175 

•0204 

•0233 

•0262 

•0291 

•0320 

•0349 

2-9 

2 

•0349 

•0378 

•0407 

•0437 

•0466 

•0495 

•0524 

2-9 

3 

•0524 

•0553 

•0582 

'0612 

•0641 

•0670 

•0699 

2-9 

4 

•0699 

•0729 

•0758 

•0787 

•0816 

•0846 

•0875 

2-9 

5 

•0875 

•0904 

•0934 

•0963 

•0992 

'IO22 

•1051 

2-9 

6 

•1051 

•I080 

•mo 

'"39 

•1169 

•1198 

•1228 

2-9 

7 

•1228 

•1257 

•1287 

•1317 

•1346 

•1376 

•1405 

2-9 

8 

•1405 

•1435 

•1465 

"1495 

•1524 

•1554 

•1584 

3'° 

9 

•1584 

•I6l4 

•1644 

•1673 

•1703 

•1733 

•1763 

3'o 

10 

•1763 

-I793 

•1823 

•1853 

•1883 

•I9H 

•1944 

3'° 

ii 

•1944 

•1974 

•2004 

•2035 

•2065 

•2095 

•2126 

3-0 

12 

•2126 

•2156 

•2186 

•2217 

•2247 

'2278 

•2309 

3*o 

13 

•2309 

•2339    • 

•2370 

•2401 

•2432 

•2462 

'2493 

3'i 

M 

•2493 

•2524 

•2555 

•2586 

•2617 

•2648 

•2679 

3'i 

15 

•2679 

•2711 

•2742 

•2773 

•2805 

•2836 

•2867 

3'i 

16 

•2867 

•2899 

•2931 

•2962 

•2994 

•3026 

•3057 

3*a 

i? 

•3057 

•3089 

•3121 

•3i53 

•3185 

•3217 

•3249 

3'2 

18 

•3249 

•3281 

•33H 

•3346 

•3378 

•34H 

'3443 

3'2 

19 

•3443 

•3476 

•3508 

•354i 

"3574 

•3607 

•3640 

3  '3 

20 

•3640 

•3673 

•3706 

'3739 

'3772 

•3805 

•3839 

3  '3 

21 

•3839 

•3872 

•3906 

"3939 

'3973 

•4006 

•4040    • 

3'3 

22 

•4040 

•4074 

•4108 

•4142 

•4176 

•4210 

•4245 

3*4 

23 

•4245 

•4279 

•4314 

•4348 

•4383 

•4417 

•4452 

3*4 

24 

•4452 

•4487 

•4522 

'4557 

•4592 

•4628 

•4663 

3'5 

25 

•4663 

•4699 

'4734 

•4770 

•4806 

•4841 

•4877 

3*5 

26 

•4877 

'49i3 

•4950 

•4986 

•5022 

•5059 

•5095 

3'6 

27 

•5095 

•5132 

•5169 

•5206 

•5243 

•5280 

•5317 

37 

28 

•5317 

'5354 

•5392 

•5430 

•5467 

•5505 

"5543 

3'8 

29 

•5543 

•558i 

•5619 

•5658 

•5696 

'5735 

'5774 

3'8 

30 

•5774 

•5812 

•5851 

•5890 

•5930 

•5969 

•6009 

3'9 

31 

•6009 

•6048 

•6088 

•6128 

•6168 

•6208 

•6249 

4-0 

32 

•6249 

•6289 

"6330 

•6371 

•6412 

•6453 

•6494 

4'i 

33 

•6494 

•6536 

•6577 

•6619 

•6661 

•6703 

•6745 

4-2 

34 

•6745 

•6787 

•6830 

•6873 

'6916 

•6959 

•7002 

4'3 

35 

•7002 

•7046 

•7089 

7133 

•7177 

7221 

•7265 

4*4 

36 

•7265 

•7310 

7355 

•7400 

7445 

7490 

'7536 

4'5 

37 

•7536 

•758i 

•7627 

7673 

•7720 

7766 

7813 

4'6 

38 

•7813 

•7860 

•7907 

7954 

'8002 

•8050 

•8098 

47 

39 

•8098 

•8146 

•8i95 

•8243 

•8292 

•8342 

•8391 

4*9 

40 

•8391 

•8441 

•8491 

•8541 

•8591 

•8642 

•8693 

5*o 

4i 

•8693 

•8744 

•8796 

•8847 

•8899 

•8952 

^9004 

5'2 

42 

•9004 

•9057 

•9110 

•9163 

•9217 

•9271 

•9325 

5  '4 

43 

•9325 

•9380 

'9435 

•9490 

'9545 

•9601 

•9657 

5'6 

44 

•9657 

•9713 

•9770 

•9827 

•9884 

•9942 

I'OOOO 

57 

APPENDIX  NO.  8.     PLANE  TABLE  MANUAL. 


449 


Table  of  corrections  for  curvature  and  refraction. 

The  correction  in  meters  for  the  combined  effect  of  curvature  and  refraction  is  given  for  each  100 
meters  distance,  the  thousands  of  meters  being  given  in  the  column  to  the  left  and  the  hundreds  in 
the  upper  line.  The  correction  is  to  be  added  to  the  difference  of  elevation  for  angles  of  elevation 
and  substracted  for  angles  of  depression,  or  it  is  always  to  be  added  to  the  uncorrected  elevation  of 
the  point  to  be  determined  from  point  of  observation. 

Example:  At  a  station  whose  elevation  is  304-80  meters  (at  telescope),  angle  to  signal  3°  eleva- 
tion, horizontal  distance  5  ooo  meters.  From  Table  V  factor  is  0-0524,  which  multiplied  by  5  ooo  = 
262-00.  From  Table  VI  correction  is  1-67  meters.  Corrected  difference  of  elevation  =  262  -oo  + 
i -67=  263-67  meters,  which  added  to  304-80  =  568-47  meters  for  elevation  of  signal.  If  the  above 
angle  to  signal  be  3°  depression,  then  corrected  difference  of  elevation  262-00  —  1*67  =  260-33  meters, 
which  makes  height  of  signal  =  304-80  —  260-33  =  44-47  meters. 

TABUS  VI. 


Distance  in 
meters 

o 

IOO 

200 

300 

400 

500 

600 

700 

800 

900 

I   OOO 

0 

O'OO 

O'OO 

O'OO 

O'OI 

O'OI 

O'O2 

O'O2 

0-03 

0-04 

0-05 

0-07 

I    OCO 

ox>7 

0-o8 

O'lO 

0*11 

0-13 

0'15 

0-17 

0-19 

O'22 

0-24 

0-27 

2   000 

0*27 

0-29' 

0-32 

0-35 

0-38 

0*42 

0'45 

0-49 

0-52 

0-56 

0*60 

3  °°° 

0*60 

0-64 

0-68 

073 

077 

0'82 

0-86 

0-91 

0-96 

I  '01 

1-07 

4  ooo 

1-07 

I'I2 

1-18 

1-23 

I  '29 

I'35 

1-41 

1-47 

I'54 

i  -60 

1-67 

5  00° 

1-67 

174 

i  -80 

1-87 

1-94 

2  -O2 

2-09 

2-17 

2-24 

2-32 

2-40 

6  ooo 

2-40 

2-48 

2-56 

2-65 

273 

2-82 

2-91 

3-00 

3-09 

3'i8 

3'27 

7  ooo 

3-27 

3-36 

3  "46 

3  '55 

3-65 

3'75 

3-85 

3-96 

4  -06 

4-16 

4-27 

8  ooo 

4-27 

4-38 

4'49 

4-60 

471 

4-82 

4-93 

5-05 

5-i6 

5-28 

5  '40 

9  ooo 

5  '40 

5'52 

5-65 

577 

5-89 

6'02 

6-15 

6-28 

6-41 

6-54 

6-67 

10  000 

6-67 

6'8o 

6-94 

7-08 

7'22 

7-36 

7-50 

7-64 

7-78 

7-93 

8-07 

II    000 

8-07 

8-22 

8-37 

8-52 

8-67 

8-82 

8-98 

9-I3 

9-29 

9-45 

9-61 

12   OOO 

9'6i 

977 

9^3 

10-09 

IO'26 

10-42 

10-59 

10-76 

10-92 

II'IO 

11-27 

13  ooo 

11-27 

ii  '45 

11-62 

ir8o 

Il-gS 

I2'l6 

12-34 

12-52 

12-71 

12-89 

13-08 

14  ooo 

13-08 

13-26 

I3-45 

13  '64 

I3-83 

14-03 

14-22 

14-42 

14-61 

14-81 

15-01 

15  ooo 

15-01 

15-21 

15-41 

15-62 

I5-82 

16-03 

16-24 

16-44 

16-65 

16-87 

17-08 

16  ooo 

17-08 

17-30 

i7'5i 

1773 

I7-95 

18-17 

i8-39 

18-61 

18-83 

19-05 

19-28 

17  ooo 

19-28 

i9'5i 

1973 

19-96 

20-I9 

20-43 

20-66 

20-89 

21-13 

21-37 

2I'6l 

18  ooo 

2I'6l 

21-86 

22'IO 

22-34 

22-58 

22-83 

23-08 

23-33 

23-58 

23-83 

24-08 

19  ooo 

24-08 

24-34 

24-60 

24-85 

25-II 

25-37 

25-63 

25-89 

26-15 

26-42 

26-68 

Comparison  of  feet  and  meters. 
[i  meter  =  3. 280869  feet.] 


Meters. 

Feet. 

Feet. 

Meters. 

I                       .... 

3-2808 

I  

o'miS 

2 

6"s6i? 

2          

0-6096 

Q*842S 

T..  . 

O'QI44 

A 

IVI2"^ 

4  

1-2192 

e 

16*4042 

5  

I  "5240 

6           

iQ'68so 

6  

1-8288 

7 

22*9658 

7.  . 

2'IT,  T,6 

8 

26*2467 

8  

2*4/";84 

2Q""~i27"*; 

q.  . 

27432 

Relief. — There  are  two  methods  of  representing  it^by  hill  shading  and  by  contours. 

Hill  shading  is  generally  effected  by  a  system  of  lines,  called  hachures,  drawn  in 
the  direction  of  the  slope.     When  it  is  steep,  the  hachures  are  thick  and  closely  spaced. 
On  the  other  hand,,  a  gentle  incline  will  be  indicated  by  fine  lines  widely  separated. 
S.  Doc.  48 29 


450 


COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 


Contours*  or  horizontal  curves  are  the  outlines  of  horizontal  sections  of  ground  at 
different  elevations  with  designated  equal  intervals  between  their  planes,  delineated  in 
their  true  positions  relatively  to  each  other  and  to  the  rest  of  the  map,  and  conforming 
to  the  scale  of  the  map  itself;  or,  briefly,  a  contour  is  the  curve  produced  by  the  intersec- 
tion of  the  horizontal  plane  with  the  surface  of  the  ground.  They  may  also  be  described 
as  imaginary  shore  lines  formed  at  stated  or  regular  elevations,  by  water  which  is  sup- 
posed to  rise  successively  to  these  elevations  over  the  face  of  the  country. 

Profile. — As  each  curve  has  equal  vertical  ordinates  at  all  points,  the  elevation  or 
profile  of  a  hill,  as  well  as  a  model  in  relief,  can  be  constructed  from  the  map,  when  it  is 
accurately  executed  on  a  large  scale,  without  further  field  measurements. 

A  profile  of  a  hill  is  the  outline  or  trace  formed  with  its  surface  by  a  vertical 
plane  cutting  the  hill  in  any  direction. 

PI.  ii  shows  the  profile  through  the  line  A'  B'  of  the  hill  H,  as  represented  on  a 
topographical  map.  The  full  parallel  lines  upon  the  profile  represent  the  successive 
heights  or  sections  of  the  hill  of  20  feet,  and  the  broken  or  intermediate  lines  x  x  x 
those  of  10  feet.  A  reference  to  the  letters  of  the  diagram  is  all  that  is  necessary  to  a 
full  understanding  of  the  subject:  a  is  the  shore  line  or  high-water  line  upon  the  map, 
xxx  are  the  auxiliary  lo-foot  curves;  f  the  coincidence  of  curves  upon  the  chart 
at  the  perpendicular  face  of  the  hill  f ,  upon  the  section.  This  is  the  only  case  where 
contours  of  different  heights  rtm  into  each  other  upon  a  topographic  plan.  D'  D'  are 
depressions  in  the  face  of  the  hill,  represented  on  the  profile  by  D  D.  d'  is  a  barranca  or 
dry  broken  gulley,  and  c'  c'  a  water  course. 

It  will  be  plain  that  if  we  were  to  suppose  the  water  to  rise  to  a  height  of  20  feet 
above  the  high- water  line,  to  h  on  the  profile,  the  2ofoot  curve  upon  the  map  would  become 
the  shore  line  and  the  depression  D'  would  fill  up  and  become  a  pond  of  water;  and  if 
the  water  were  to  rise  to  a  height  of  30  feet,  the  dotted  broken  line  would  form  a  shore 
line,  and  the  knoll  G  would  become  an  island. 

Advantages  and  disadvantages  of  hill  shading  and  contours. — -In  a  mountainous 
country  the  method  of  hill  shading  presents  a  picture  which  expresses  more  forcibly  to 
the  eye  the  configuration  of  the  country  than  a  system  of  contours.  But  the  objection 
to  its  sole  use  arises  from  the  fact  that  although  one  ridge  is  perceived  to  be  higher  than 
another,  there  is  ho  guide  for  stating  in  terms  of  some  linear  unit  this  difference  in  ele- 
vation. It  also  obscures  the  symbols  representing  other  details  on  the  surface. 

A  system  of  contours  furnishes  a  convenient  means  for  obtaining  the  heights  on  any 
part  of  a  map,  but  does  not  adapt  itself  to  the  representation  of  the  small  but  important 
accidents  of  the  ground,  such  as  gullies,  ledges,  rocks,  etc. ;  nor  does  it  satisfactorily 
delineate  such  features  as  cliffs,  bluffs,  quarries,  railroad  cuts,  and  embankments. 

For  these  reasons  the  United  States  Coast  and  Geodetic  Survey  has  adopted  both 
methods;  employing  hachures  for  the  smaller  features  and  where  the  steepness  of  the 
slope  would  make  the  contour  lines  approach  together  so  closely  that  individual  lines 
would  become  indistinguishable,  and  relying  on  the  contours  to  delineate  less  precipitous 
ground. 

The  two  systems  can  be  seen  combined  when  it  is  necessary  to  indicate  a  rocky  and 
broken  mountain  face.  (Pis.  12  and  13.) 

*For  interesting  articles  on  the  diagrammatic  properties  of  the  contour  line  see:  On  Contour  and 
Slope  Lines,  Cayley,  London  &  Ed.  Mag.,  1859,  pp.  264-268;  On  Hills  and  Dales,  Clerk  Maxwell, 
ibid,  1870,  pp.  421-426;  Properties  of  Matter,  Tait,  1890,  pp.  70-81. 


Coast  caul  Geodetic  Survey  Report  2897  38  Appendix  8 


Moll 


iUustraJtiruj  Phjf,  mode  of  conjstruuctinq  J*rafiLe  from 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  451 

The  contour  interval  customarily  used  on  the  Coast  and  Geodetic  Survey  field  sheets 
is  20  feet.  When,  however,  the  contour  runs  very  near  to  some  remarkable  accident 
of  ground,  as  a  prominent  spur  or  indentation,  a  slight  deviation  above  or  below  its  true 
plane  is  admissible  to  include  this  feature,  although  it  is  preferable  to  avoid  doing  so,  if 
possible,  by  the  introduction  of  an  auxiliary  curve. 

In  abruptly  mountainous  and  comparatively  inaccessible  regions,  where  sketching 
must  be  relied  upon,  loo-foot  curves  may  suffice  to  develop  all  necessary  features. 

Datum  plane. — Probably  the  best  plane  of  reference  for  heights  of  points  on  the 
earth's  surface  is  the  mean  level  of  the  sea,  since  the  mean  of  the  rise  and  fall  of  the  tides 
is  approximately  this  level.  In  practice,  however,  mean  high  water  is  usually  taken,  as 
it  includes  all  land  not  covered  by  the  tide  range,  and  is  the  line  dividing  land  and  water. 

Reference  signal. — It  is  advisable  in  commencing  the  survey  of  a  region  bordering 
on  tide  water  to  locate  one  or  more  signals  at  the  assumed  high-water  line,  carefully 
noting  the  height  of  the  top  of  the  flag  above  the  same,  to  be  used  for  observing  angles 
of  depression  upon  for  heights  from  points  occupied  during  the  progress  of  the  graphic 
triangulation.  As  the  heights  of  other  points  are  determined  in  the  course  of  the  survey 
and  verified  from  observations  from  two  or  three  other  points,  these  in  turn  may  be  used 
for  the  same  purpose. 

Regular  and  irregular  methods  of  contouring . — The  two  methods  of  surveying  curves 
of  equal  elevation  are  known  as  the  Regular  and  the  Irregular  methods. 

The  Regular  methods  include — 

1 .  Surveying  and  leveling  the  skeleton  and  its  traverses. 

2.  Surveying  and  leveling  the  profile  lines.    •"' 

3.  Surveying  and  leveling  the  base  of  each  level  section. 

4.  Surveying  and  leveling  the  parts  of  several  level  sections  from  one  station. 

5.  The  division  of  the  terrene  into  squares,  triangles,  or,  parallelograms. 

The  profile  is  a  traverse  line  on  which  are  determined  the  heights  of  the  points  at 
which  the  surface  changes  slope.  The  points  where  this  line  is  intersected  by  the  suc- 
cessive level  equidistances  are  with  the  level  and  rod  easily  determinable.' 

To  determine  the  base  of  each  level  section  the  table  is  set  up  in  position  where  this 
level  intersects  the  profile,  and  using  the  alidade  as  a  leveling  instrument,  with  the  tar- 
get fixed  on  the  staff  at  the  height  of  the  optical  axis  of  the  telescope,  the  line  is  traced 
by  locating  the  rod  by  successive  steps  at  characteristic  points  of  the  terrene,  when  the 
target  comes  in  the  horizontal  plane  of  the  optical  axis,  direction  and  distance  of  the 
rod  being  determined  and  drawn  in  each  case.  A  line  drawn  through  these  points, 
recognizing  features  between  the  stations,  locates  the  curve.  In  this  operation  allow- 
ance should  be  made  for  curvature  and  refraction,  when  the  distance  becomes  sufficiently 
great  to  make  it  a  factor. 

When  parts  of  several  level  sections  are  run  from  one  station,  set  up  the  table  at  a 
point  in  an  equidistance  curve,  and  observe  on  the  staff  the  height  of  the  optical  axis  of 
the  alidade.  Set  the'  target  on  the  staff  above  this  height  as  many  equidistauces  as  its 
length  will  include.  The  aid  carries  the  staff  below  the  instrument  and  is  signaled  to 
stop  when  the  target  comes  in  the  horizontal  plane  of  the  optical  axis,  and  at  successive 
steps  traverses  the  lower  curve.  The  target  is  then  lowered  on  the  staff  one  equidistance 
and  the  next  curve  above  is  in  the  same  manner  traced,  continuing  the  proceeding  until 
the  level  of  the  instrument  is  reached,  when  the  table  is  moved  to  an  upper  station  and 
the  proceeding  continued  until  the  summit  is  reached. 


452  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

By  the  mode  of  regular  division  of  the  surface  into  squares,  triangles,  or  parallelo- 
grams, pegs  are  driven  at  regular  intervals,  and  their  heights  determined  by  level  in  the 
way  that  may  be  most  convenient,  a  spirit-leveling  instrument  being  the  most  accurate. 

The  Irregular  method  consists  in  determining  the  positions  and  heights  of  a  number 
of  characteristic  points  of  the  terrene,  and  in  determining  from  these  the  traces  of  the 
curves. 

This  is  the  method  generally  used  in  surveys  embracing  such  areas  as  the  sheets  of 
the  Coast  and  Geodetic  Survey  on  scales  of  T^oo  anc*  2 ffffo fl- 
it has  the  merit  that  the  development  of  the  terrene  proceeds  with  the  survey  of 
the  skeleton,  and  does  not  necessitate  a  return  to  a  station  when  once  occupied.  In 
connection  with  the  determination  of  position  by  resection  it  works  harmoniously  and 
economically,  since  points  that  would  be  selected  for  position  as  having  the  best  outlook 
are  likely  to  be  the  characteristic  ones  of  the  terrene. 

Station  routine. — The  topographer  having  determined  his  position  on  the  sheet, 
and  also  the  height  of  the  instrument,  he  proceeds  to  map  the  natural  and  artificial 
details  of  the  area  surrounding  the  station.  For  this  purpose  the  direction  of  each 
detail  is  obtained  by  pointing  the  telescope  upon  it,  the  edge  of  the  rule  cutting  the 
station  point;  its  distance  by  reading  the  stadia  rod  held  there  for -the  purpose.  This 
distance  is  then  taken  off  the  metal  scale  with  a  pair  of  dividers  and  plotted  along  the 
edge  of  the  rule. 

While  this  is  in  progress,  the  alidade  is  used  both  as  a  level  for  the  observation  of 
objects  of  the  same  height  as  the  instrument,  and  for  measuring  angles  of  elevation  and 
depression  to  such  of  the  plotted  details,  whose  position  at  critical  points  of  the  contours 
would  materially  assist  the  topographer  in  tracing  them. 

Number  of  elevations  to  be  determined. — No  rule  can  be  laid  down  as  to  the  number 
of  elevations  that  should  in  this  manner  be  determined  from  each  plane  table  station  or 
for  a  given  area.  It  will  depend  on  the  skill  of  the  topographer  and  the  modeling  of 
the  ground.  The  number  will  be  adequate  when  he  is  confident  of  tracing  by  their  aid 
the  contours  with  an  accuracy  sufficient  for  the  scale  and  the  purpose  of  the  survey. 

It  would  indicate  careless  and  slovenly  work  if  the  contours  were  found  on  exam- 
ination to  deviate  frequently  from  their  true  position  on  the  sheet  by  more  than  half  an 
interval  for  a  slope  of  less  than  5°  in  an  open  country.  When  the  slope  is  steeper,  or 
in  wooded  regions,  a  greater  latitude  is  permissible,  but  even  here  in  representing  the 
crests  of  ridges,  prominent  hill  tops,  and  valley  floors,  this  limit  of  half  an  interval  should 
not  be  departed  from  for  good  work.* 

Contour  sketching. — The  topographer  will  be  assisted  in  sketching  contours,  where 
the  modeling  is  intricate,  by  lightly  drawing  a  skeleton  composed  of  the  ridge  lines  and 
thalweg  lines  (lowest  lines  of  valleys)  in  their  proper  positions  around  the  station.  On 
the  ridge  lines  will  be  found  the  extreme  outward  or  convex  bends  of  the  contours,  and 
on  the  thalweg  lines  the  extreme  inward  or  concave  bends. 

It  can  be  readily  imagined  that  if  each  spur  and.  each  small  depression  was  repre- 
sented by  its  appropriate  line,  and  on  each  of  them  were  located,  either  by  observation 

*  For  some  pertinent  remarks  on  this  subject  see  Bulletin  of  the  University  of  Wisconsin,  Eng. 
Series,  Vol.  i,  No.  10,  Topographical  Surveys.  Their  methods  and  values,  J.  F.  Van  Ornum,  pp. 
360-361. 


Coast  and.  Geodetic  Survey  Report  1897-9H.  Appendix  8. 


No.12 


Crest.  Frwc  cine/.  TaJus  of  a  Gr-u,ru,i,e  COW.  (Eagljt*  Cliff,  Mt..  Desert  I.) 


.  PNOTO-LITMO     WASHINGTON. 


2 

te' 
G 


'or 

9J 


Coast  and  Geodetic  Survey  Report  189  7 '98   Appendix  8. 


No.  14 


Fig 


Fig.  22 


Fig.  23 


Fig.  25 


Fig.  24 


i.  27 


Typical  Contour  Groups 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  453 

or  estimation,  points  having  elevations  equal  to  some  multiple  of  the  contour  interval, 
it  would  be  .only  necessary  to  connect  those  points  having  the  same  elevation  with  a 
smooth  curve  to  have  a  correct  plan  of  the  contours. 

It  will  simplify  the  sketching  at  a  station  to  draw  the  highest,  lowest,  and  middle 
contours  first,  as  they  will  then  serve  as  guides  for  estimating  the  position  of  the  others. 

It  should  be  remembered  that  a  contour  never  splits,  as  shown  in  PI.  14,  fig.  20; 
nor  do  two  contours  run  into  one,  as  shown  at  fig.  21 ;  nor  cross  each  other,  except  in 
the  rare  instance  of  an  overhanging  cliff,  as  shown  in  fig.  22. 

When  an  auxiliary  contour  is  introduced,  no  more  of  it  is  drawn  than  is  sufficient 
to  delineate  the  special  feature  which  makes  it  necessary.  A  principal  contour,  on  the 
other  hand,  can  not  have  an  end  within  the  map ;  if  it  commences  at  one  edge  it  must 
terminate  at  another. 

Typical  contour  groups. — A  closed  contour  encircled  by  one  or  more  closed  contours 
is  either  a  hill,  as  shown  in  fig.  23,  PI.  14,  or  a  depression,  as  shown  at  fig.  24;  the 
arrows  showing  the  direction  in  which  water  would  run.  The  summits  of  all  the  hills 
of  importance  should  have  their  elevations  determined  and  marked  on  the  map.  All 
depressions  without  an  outlet  and  which  do  not  contain  a  pond  or  lake  should  be 
marked  with  a  D  at  their  lowest  point. 

A  series  of  contours,  as  shown  in  fig.  25,  is  either  a  croupe  (the  end  of  a  ridge  or 
promontory)  or  a  valley.  If  a  croupe,  the  contours  will  have  their  concave  sides 
toward  the  higher  ground ;  if  a  valley,  the  contours  will  have  their  concave  sides 
toward  the  lower  ground. 

A  combination  of  four  sets,  like  fig.  26,  with  convex  sides  turned  toward  each  other, 
represents  a  dip  in  a  ridge,  or  the  junction  of  two  ridges,  and  is  called  a  saddle. 

A  pass  in  a  mountain  range  generally  takes  the  form  shown  in  fig.  27. 

Order  of  development  of  contours. — As  the  progress  of  topographical  work  is  usually 
from  the  shore  line  inward,  this  affords  the  most  favorable  direction  for  drawing  the 
curves  of  equal  elevation,  and  as  it  is  desirable  that  all  work  at  a  station  shall  be  com- 
pleted when  it  is  first  occupied,  so  as  to  avoid  the  necessity  of  returning  to  it,  the  curves 
should  be  drawn  by  the  eye  from  the  shore-line  to  the  points  sighted  and  determined 
for  position  and  height,  to  be  checked  by  reverse  drawing  from  those  points  when  in 
turn  occupied;  and  so  from  station  to  station,  drawing  to  and  from  in  reverse  will  check 
and  verify,  between  stations  not  too  far  apart,  such  comparatively  small  errors  of  position 
as  an  accurate  eye  will  soon  learn  to  estimate.  The  heights  of  sufficiently  close  points 
must  be  determined  to  guard  against  any  wide  range  of  estimate  of  height  by  the  eye. 

In  abrupt  slopes  of  considerable  extent  the  use  of  a  pocket  clinometer  is  of  much 
value  to  determine  the  degree  of  slope,  and  to  draw  accordingly  the  curves  by  the  widths 
of  their  zones  (the  cosines  of  angles  of  slope)  from'a  paper  scale  prepared  for  the  pur- 
pose. (See  PI.  30.) 

Filling  in. — Having  completed  the  work  at  a  given  station,  the  topographer  proceeds 
with  his  party  and  instruments  to  an  adjoining  locality,  where  he  selects  a  new  station 
from  which  he  can  gather  the  details  of  an  area  bordering  upon  the  one  last  surveyed. 
In  this  manner,  by  successively  occupying  stations  over  the  whole  expanse  of  the  sheet, 
the  skeleton  map  is  filled  in. 

Traverse  lines. — In  a  wooded  country,  where  it  is  impossible  to  find  open  space  with 
range  sufficient  to  see  enough  points  for  determination  of  position  by  resection,  it  is 


454  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-96. 

necessary  to  run  traverses  along  the  roads,  with  offsets  to  such  lateral  features  as  it  may 
be  practicable  to  reach  without  the  expenditure  of  excessive  labor  and  time  in  opening 
lines  of  sight.  The  levels,  when  necessary,  are  carried  along  with  the  line  by  observing 
the  vertical  angles  with  the  alidade  upon  some  mark  on  the  rod,  taking  back  and  fore 
sights  at  alternate  stations. 

Main  traverse. — The  standard  table  is  used  on  main  roads  and  whenever  the  details 
are  important  and  numerous. 

The  traverse  line  is  started  by  occupying  some  point  previously  determined  and 
sending  the  telemeter  rod  ahead  to  a  place  selected  for  its  advantageous  position,  in 
reference  either  to  the  surrounding  features,  or  facility  in  obtaining  a  new  section  of  the 
traverse. 

Having  sighted  to  this  point,  read  and  plotted  the  distance,  short  guide  lines  should 
be  drawn  along  the  edge  of  the  ruler  at  both  ends  and  numbered  or  lettered,  so  they 
may  be  identified  from  others  of  like  character.  The  table  is  then  moved  to  the  forward 
station,  approximately  oriented  with  the  eye,  and  the  plotted  point  carefully  plumbed 
over  the  one  on  the  ground. 

The  alidade  is  now  placed  on  the  table,  and  the  table  oriented  by  bringing  the  edge 
of  the  ruler  close  up  £o  the  guide  lines;  then  revolving  the  table  until  the  vertical  wire 
bisects  the  rod  or  signal  left  for  that  purpose  at  the  last  station. 

The  same  processes  which  were  employed  at  the  initial  station  are  now  repeated; 
the  detail  mapped  and  the  new  station  in  advance  occupied  in  turn;  the  line  progressing 
in  this  manner  by  successive  steps. 

In  running  traverses,  great  care  should  be  taken  to  sight  as  low  as  possible  upon 
the  fore  and  back  signals,  so  as  to  avoid  any  error  of  deflection  which  might  arise  from 
the  inclination  of  the  signal  poles. 

Subordinate  traverse. — When  the  line  is  unimportant  and  few  features  present  them- 
selves to  be  noted,  an  auxiliary  plane-table  oriented  by  a  declinatoire  or  a  transit,  fitted 
with  stadia  wires,  may  be  employed. 

When  this  method  is  pursued  with  a  second  table  the  forward  rod  station  is  not 
occupied,  but  another  is  chosen  in  advance  of  it,  from  which  it  can  be  .seen  where  the 
instrument  is  set  up  and  oriented  with  the  declinatoire.  Sighting  the  alidade  to  what 
is  now  the  back  station,  the  distance  is  read  and  plotted  along  the  edge  of  the  ruler, 
and  the  point  so  determined  represents  the  one  occupied  by  the  table. 

The  pivot  on  which  the  declinatoire  needle  rests  should  be  examined  frequently,  the 
least  roughness  as  to  its  point  will  cause  the  needle  to  drag  and  introduces  serious  de- 
flections in  azimuth. 

All  traverse  lines  should  start  and  end  at  well-determined  points.  This  will  serve 
to  check  the  accuracy  of  the  work.  .  If  the  closing  error  is  not  too  large,  the  line  should 
be  adjusted  by  distributing  it  throughout  its  length.  The  line  is  run  on  a  spare  sheet 
when  an  auxiliary  table  is  used;  then  traced,  "swung  in,"  and  adjusted  between  the 
two  fixed  points. 

Determinations  for  hydrography. — Where  the  topography  surveyed  includes  the  shore- 
line of  a  body  of  water,  the  hydrographic  survey  of  which  is  intended  to  follow  the  topo- 
graphical work,  as  in  the  Coast  Survey,  it  is  the  duty  of  the  topographer  to  locate  and 
determine  the  shore  signals,  and  it  is  only  necessary  to  state  that  they  should  be  so  placed 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  455 

as  to  furnish  the  hydrographic  party  \vith  as  many  points  as  is  desirable  for  the  deter- 
mination of  positions  on  the  water. 

Natural  or  artificial  objects  along  the  shore,  or  in  plain  sight  from  the  water,  such  as 
fence  ends,  rocks,  prominent  houses,  etc. ,  should  be  determined  and  marked  upon  the  sheet. 

Lines  to  buoys  and  other  permanent  floating  objects  should  be,  as  far  as  practicable, 
taken  at  the  same  stage  of  the  tide,  or  direction  of  current. 

The  delineation  of  the  ordinary  mean  low- water  mark  should  be  aimed  at,  and  when 
it  is  beyond  the  reach  of  the  plane-table,  and  presents  no  marked  points  for  determination, 
or  is  of  a  character  that  will  not  admit  of  putting  up  and  working  the  instrument — as 
along  the  swampy  shores  of  the  south,  where  the  muddy  shoals  extend  far  seaward,  and 
among  the  shifting  quicksands  of  our  great  estuaries  and  bays — it  may  be  left  to  be  traced 
by  the  soundings  and  tidal  reductions  of  the  hydrographic  parties.  The  channels  through 
mud  flats  of  this  character  should  be  indicated,  however,  if  only  approximately,  by  cuts 
and  tangents,  or  the  determination  of  stakes  at  the  turning  points.  Where  the  fall  of 
the  tide  exposes  rocks  and  ledges,  shingle  beaches,  etc.,  their  character  and  extent  should 
be  delineated  and  distinguished  from  the  sandy  beaches,  as  these  are  features  most  diffi- 
cult and  laborious  for  the  hydrographic  survey  to  represent. 

High-water  and  storm-water  line. — In  tracing  the  shore  line  on  an  exposed  sandy 
coast  care  should  be  taken  to  discriminate  between  the  average  high-water  line  and  the 
storm- water  line. 

Determination  of  inaccessible  points . — On  a  precipitous  coast,  \vhere  the  shore  line  is 
inaccessible  and  can  not  be  determined  by  ordinary  methods,  the  salient  features  are 
located,  when  occupying  commanding  stations,  by  observing  the  vertical  angles  upon 
them,  and  drawing  direction  lines  to  them.  Then  using  the  elevation  of  each  station 
as  a  base  the  distance  to  each  feature  is  computed  and  plotted. 

The  same  method  applies  to  outlying  rocks,  and  is  often  employed  where  there  is 
any  doubt  of  their  being  identified  from  different  places. 

Large  scale  surveys. — As  has  been  previously  stated,  i-io  ooo  and  1-20  ooo  are  the 
scales  customarily  used  in  the  execution  of  the  topographical  work  of  the  United  States 
Coast  and  Geodetic  Survey,  as  they  are  the  ones  best  suited  for  the  charting  of  the 
coast  line  and  harbors  of  the  United  States. 

Other  surveys  for  special  purposes  have  been  made  from  time  to  time  on  scales 
both  larger  and  smaller,  and  the  field  practice  has  been  modified  according  to  the  require- 
ments of  the  scale  used. 

A  topographical  survey  of  the  District  of  Columbia  outside  the  thickly  populated 
limits  of  the  City  of  Washington  was  made  between  the  years  of  1880  and  1891  on  a 
scale  of  1-4  800. 

The  methods  pursued  are  here  described,  as  they  are  typical  of  other  surveys  on  a 
large  scale. 

Based  on  a  sufficiently  minute  triangulation,  the  plane-table  and  stadia,  wye  level, 
and  rod  were  used  for  all  determinations  of  details.  The  relief  was  elaborately  indicated 
by  contour  intervals  of  5  feet.  The  datum  plane  is  the  same  as  used  by  the  engineer 
department  of  the  District,  on  which  is  based  all  the  levels  used  for  grades  of  streets  and 
sewers  in  the  city  of  Washington,  the  survey  being  made  for  the  purpose  of  extending 
streets  and  avenues  beyond  the  city  limits. 


456  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

From  this  datum,  along  all  roads,  avenues,  and  railroads,  and  where  roads  were 
infrequent,  across  country,  lines  of  level  were  run,  and  after  careful  checking  in  the 
usual  manner  bench  marks  were  placed  in  position  convenient  to  all  parts  of  the  field. 

The  plane-table  stations  were  established  so  as  to  easily  overlook  every  part  of  the 
field  and  so  close  together  that  each  was  surrounded  by  the  others  within  the  range  of 
a  single  reading  of  the  stadia  rod. 

The  mode  of  procedure  was  as  follows: 

The  plane-table  was  placed  in  position  by  a  graphic  solution  of  the  three-point 
problem.  At  the  same  time  the  height  of  the  level  was  determined  above  some  near 
bench  mark  and  the  target  of  the  level  rod  fixed,  so  that  when  it  was  in  the  line  of  sight 
of  the  level  the  bottom  of  the  rod  would  rest  on  the  ground  where  the  elevation  corre- 
sponded to  that  of  some  contour.  The  level  rodsman  then  began  his  journey  along  this 
imaginary  horizontal  line,  holding  the  rod  for  the  observation  of  the  levelmau  at  each 
noticeable  change  in  the  configuration  of  the  ground.  The  levelman  directed  the  rods- 
man by  signals  at  each  point  until  the  rod  was  in  position  on  the  contour  line,  when  the 
stadia  rod  was  substituted  and  its  distance  read  and  plotted  on  the  plane-table  sheet. 
Both  rodsmen  followed  the  contour  line  in  both  directions  from  the  table  as  far  as  the 
stadia  rod  could  be  conveniently  read.  Generally  two  and  sometimes  three  contours 
were  run  from  one  level  station,  and  on  their  completion  a  turning  point  was  fixed  and 
the  level. shifted  to  a  higher  or  lower  ground,  as  the  circumstances  required. 

A  survey  of  Craney  Island,  Virginia,  was  made  in  the  same  manner  on  a  scale  of 
i-i  200. 

RAPID  SURVEYS. 

Military  reconnaissance. — In  almost  every  field  of  operations,  from  the  commence- 
ment of  the  civil  war  to  its.  close,  the  plane-table  was  used. 

Until  this  time  very  little  was  known,  save  in  theory,  of  the  value  of  the  plane  table 
as  a  reconnoitering  instrument,  and  it  is  the  testimony  of  all  the  officers  of  these  parties, 
as  the  result  of  their  labors,  that  for  rapidity  and  accuracy  in  the  execution  of  military 
reconnoissance  it  is  more  effective  than  any  other  instrument. 

The  usual  system  adopted,  in  default  of  triangulation,  was  the  measurement  of  a 
base  with  an  ordinary  chain  and  triangulating  with  the  plane  table. 

In  detailed  surveys  for  the  Army,  where  a  topographer  averages  from  i  to  3  square 
miles  a  day,  on  large  scales  a  chained  base  of  from  one-half  to  three-quarters  of  a  mile 
for  the  survey  of  an  area  of  25  square  miles  is  found  sufficient. 

At  Chattanooga,  from  two  different  bases  of  about  half  a  mile  each,  platted  on 
separate  sheets,  and  measured  once  carefully  with  the  common  2o-meter  chain,  the 
same  chain  being  used  -for  both  measurements,  after  considerable  intermediate  plane- 
table  triangulation  carried  on  by  two  officers,  two  objects  were  determined  2}^  miles 
apart,  common  to  both  sheets,  which  were  on  a  scale  of  75500.  and  the  discrepancy  was 
but  about  15  meters.  Many  other  points  of  junction  indicated  this  to  be  the  maximum 
error.  In  this  case  the  leaves  were  mostly  off  the  trees  and  the  hills  afforded  good 
points.  The  sheets  covered  about  20  square  miles  each.  At  Nashville  there  was  a 
discrepancy  of  about  10  meters  in  2  miles. 

At  other  times,  when  the  character  of  the  country  or  the  pressure  of  time  did  not 
admit  of  the  measurement  of  a  preliminary  base  and  topographical  triangulation,  the 


APPENDIX  NO.  8.  PLANE  TABLE  MANUAL,.  457 

work  was  commenced  by  starting  from  a  single  point  and  prosecuted  by  linear  measure- 
ment with  the  chain  or  stadia,  intersections  from  the  ends  of  the  chained  lines  being 
taken  to  determine  objects,  which,  as  the  work  progressed,  could  also  be  used  as  checks 
upon  tlie  chaining.  Where  circumstances  permitted,  an  occasional  return  with  the 
chain  to  a  back  point,  either  to  close  a  series  of  lines  upon  it  or  to  start  afresh,  was 
resorted  to.  This  work  was  generally  carried  on  over  roads  and  the  interior  filled  in  by 
sketching  and  intersection  as  far  as  practicable.  Some  of  the  tests  in  this  latter  work, 
where  the  operations  of  two  officers  joined,  were  remarkably  close. 

A  very  efficient  topographical  officer  estimates  that  with  the  usual  number  of  hands 
and  a  good  sketcher  for  aid,  in  a  country  of  average  variety  of  detail,  in  which  all  the 
houses,  prominent  barns  and  outbuildings,  streams,  roads,  general  outline  of  woods,  and 
approximate  curves  are  to  be  shown,  on  a  scale  of  TT^TTO.  an  area  of  between  2  and  3 
square  miles  can  be  filled  in  daily,  with  not  only  sufficient  accuracy  for  military  pur- 
poses, but  so  that  an  accustomed  eye  with  ' '  the  map  in  hand  would  not  discover  any 
marked  discrepancy." 

This  rapidity  of  work,  however,  could  not  be  expected  in  or  near  towns  or  populous 
districts.  It  is  doubtful  if  the  average  work  would  reach  more  than  one-half  this  amount. 

In  some  thickly  wooded  sections  and  where  time  is  limited,  it  has  been  found 
advisable  to  run  the  main  roads  with  the  plane  table  and  fill  up  with  the  compass,  which 
is  more  rapid  but  less  accurate  than  where  the  entire  work  is  done  with  the  plane  table 
alone.  The  usual  method  employed  where  these  methods  were  combined,  was  as  follows: 
Where  the  army  was  stationary,  or  moving  leisurally,  one  main  road  was  run  with  the 
plane  table,  the  operator  being  accompanied  by  assistants  well  practiced  in  the  use  of 
the  compass.  Upon  arriving  at  any  important  road  or  water  course  an  assistant  'was 
sent  to  the  right  and  left,  starting  from  a  plane-table  point,  determined  by  the  chaining, 
and  running  as  far  as  was  requisite  and  then  returning  to  the  main  road  again  to  repeat 
the  operation,  the  compass  notes,  of  course,  being  kept  in  a  book  prepared  for  the  pur- 
pose. Prominent  points  determined  by  the  plane  table  were  used  as  checks  in  the 
compass  work.  The  intervening  topography,  where  no  compass  or  plane-table  work 
had  been  done,  was  sketched  in  by  the  chief  of  the  party,  in  which  accurate  pacing 
became  of  great  value. 

With  compass  and  notebook. — Plane-table  methods  can  be  utilized  to  advantage 
when  compass,  pencil,  notebook,  and  ruler  are  the  substitutes  for  an  instrumental  outfit. 
The  book  serves  as  the  sheet  and  board  combined,  and  the  ruler,  as  it  was  in  the  early 
days  of  the  art,  becomes  the  alidade.* 

Photogrammetry '.f — In  the  topographical  reconnoissance  made  for  the  Alaska 
Boundary  Survey  by  the  Coast  and  Geodetic  Survey,  the  camera  with  constant  focal 
length  has  been  used  as  an  adjunct  to  the  small  mountain  plane  table.  The  latter  was 
used  to  plat  the  shore  line  and  adjacent  topography,  also  to  determine  as  many  peaks 
of  the  interior  country  as  possible  by  the  intersection  of  lines  of  direction.  All  camera 
stations  were  determined  geographically  and  hypsometrically,  and  platted  upon  the 

*  See  "Sketching  without  instruments,"  in  Topography,  Drawing,  and  Sketching,  by  Lieut.  Henry 
A.  Reed,  U.  S.  A.,  1886. 

t  See  United  States  Coast  and  Geodetic  Survey  Report,  1893,  App.,  3,  and  Report  for  1897. 
Photo-Topographic  Methods  and  Instruments,  Flemer. 


458  COAST  AND  GEODETIC  SURVEY  REPORT,   1897-98. 

plane-table  sheet.  The  topographical  details  beyond  the  reach  of  the  plane  table  were 
added  to  the  map  in  the  Office  by  the  photogrammetric  methods. 

The  rugged  mountains  of  southeast  Alaska  appear  particularly  well  adapted  for 
this  mode  of  procedure,  as  identical  points  can  be  readily  picked  out  from  different  pan- 
orama views,  owing  to  the  characteristic  shapes  of  the  mountain  peaks,  snow  fields, 
glaciers,  etc. 

Periods  of  fair  weather  are  also  very  short  and  of  rare  occurrence  in  that  locality, 
and  a  great  deal  of  topographical  material  can  be  gathered  photographically  in  a  short 
time,  which  when  platted  will  cover  a  large  territory  jf  a  sufficient  number  of  reference 
points  on  the  views  have  been  located  instrumentally. 

The  platting  proper  can  be  carried  out  to  any  degree  of  minuteness  and  detail;  the 
only  requirement  is  that  a  sufficient  number  of  camera  stations  shall  have  been  occupied 
to  fully  cover  the  territory  in  question,  so  that  every  topographical  feature  of  prominence 
has  been  seen  or  photographed  from  at  least  two  stations — better  more. 

By  this  application  of  photogrammetry  the  plane-table  methods  of  determining 
topographical  details  are  extended  to  the  Office,  inasmuch  as  the  same  features  are 
selected  from  the  panorama  views  and  platted  geographically  which  would  have  been 
located  by  the  plane  table.  But  the  actual  time  .spent  in  the  field  is  reduced  at  the 
expense  of  the  time  needed  for  office  work. 

Survey  in  advance  of  triangulation. — Where  it  is  necessary  to  make  a  topographical 
survey  in  advance  of  the  determination  of  points  by  triangulation,  a  reconnoissance  is 
first  made  for  the  location  of  a  base  line  and  selection  of  points  to  be  determined  with 
the  plane  table. 

The  base  is  measured  with  sufficient  accuracy  and  conveniently,  with  a  steel  tape 
which  has  been  compared  with  a  standard  at  a  fixed  tension,  and  to  one  end  of  which  is 
attached  a  spring  balance  to  secure  the  same  tension  during  measurement.  The  suc- 
cessive lengths  are  marked  by  lines  cut  on  copper  tacks  driven  in  wooden  stubs  firmly 
set  in  the  ground.  The  temperature  is  noted  at  frequent  intervals  as  the  work  progresses, 
and  the  corrections  are  applied  to  the  length  of  the  base  when  completed. 

The  base  .is  then  properly  located  on  the  sheet  in  reference  to  the  area  to  be 
embraced  and  its  length  carefully  set  off.  It  is  well  at  the  same"  time  to  mark  in  three 
or  four  different  parts  of  the  sheet  lengths  of  i  ooo  meters  for  the  purpose  of  determin- 
ing at  any  time  the  true  scale  of  the  sheet  variable  by  the  different  hygrometric  condi- 
tions of  the  atmosphere. 

Signals  having  been  erected  at  the  selected  points,  the  extremes  of  the  base  are 
occupied  with  the  table  and  the  points,  as  far  as  maybe  reached  with  good  intersections, 
determined  from  them  and  lines  of  direction  drawn  to  all  the  points  visible,  to  serve  as 
checks  upon  their  determination  from  other  points  furnishing  directions  for  good  inter- 
sections. The  survey  then  proceeds  as  usual. 

It  is  well  at  the  beginning  of  work  to  set  off  with  the  declinatoire  at  some  deter- 
mined point  near  the  middle  of  the  sheet  the  magnetic  meridian,  for  the  purpose  of  put- 
ting the  table  in  approximate  position  at  any  station  with  the  declinatoire.  The  manner 
of  doing  this  is  elsewhere  described. 

Before  finishing  the  field  work  it  is  important,  when  the  sheet  has  no  projection,  to 
provide  data  for  drawing  a  true  north  and  south  line.  This  is  done  by  drawing  from 
a  point  upon  the  sheet,  when  the  table  is  in  position,  a  line  in  the  vertical  plane  through 


APPENDIX  NO.  8.     PLANK  TATU.K  MANUAL. 


459 


Polaris  and  the  point  occupied  and  recording  the  time  of  observation.  The  a/.hmith  of 
the  star  at  that  time  being  known,  a  true  north  and  south  line  can  accordingly  be  set  off. 

If  a.  small  transit  instrument  is  at  hand  and  carefully  adjusted  for  movement  in 
vertical  plane,  an  assistant  with  a  lantern  can  be  located  where  the  vertical  plane  through 
Polaris  and  the  point  occupied  intersects  the  ground,  at  as  great  a  distance  from  the 
point  as  the  ground  will  admit  of  within  the  limit  of  communication  by  light  signals. 
When  the  assistant  is  in  position,  a  stake  is  there  driven,  the  direction  to  which  from 
the  point  occupied  may  be  determined  by  daylight. 

If,  in  the  absence  of  a  transit,  the  alidade  has  not  vertical  range  sufficient  to  reach 
Polaris,  ail  illuminated  plumb  line  may  be  used  for  the  alignment. 

OFFICK  WORK. 

All  the  drawing  of  the  topographical  features  of  a  siirve)^  upon  the  chart  should  be 
penciled  in  the  field,  while  they  are  still  under  the  eye.  Sketching  and  plotting  in  the 
office  from  notes,  unless  the  country  be  near  at  hand  for  ready  reference  in  case  of  doubt 
or  a  defective  sketch,  is  objectionable.  Where  this  is  unavoidable,  the  sketch  should  be 
transferred  to  the  sheet  as  soon  as  possible  after  having  been  taken,  while  it  is  fresh 
in  the  mind  of  the  person  by  whom  it  was  made,  and  by  whom,  also,  if  possible,  it  should 
be  plotted.  Days  which,  from  inclemency  of  the  weather,  are  unfavorable  for  out-of- 
door  work  should  be  allotted  to  this  purpose,  and  advantage  should  be  taken  of  them, 
also,  for  retouching  any  details  of  the  sheet  which  may  have  become  indistinct,  as  it  is 
very  important  that  they  should  not  be  left  indefinite  or  become  obliterated;  for  when 
the  inking  is  done,  as  it  generally  is,  at  a  distance  from  the  field  of  operations,  the 
necessity  for  this  care  is  obvious.  Nos.  4  and  5  pencils  are  good  for  this  purpose,  for 
which  very  hard  or  very  soft  and  black  pencils  are  equally  unsuited. 

In  the  inking  of  a  topographical  sheet  three  requisites  to  its  proper  appearance 
when  finished  should  be  borne  in  mind:  clearness,  neatness,  and  uniformity. 

The  lines  and  objects  should  be  clean  and  sharply  defined,  nothing  being  left  obscure 
or  doubtful;  the  paper  should  be  kept  unsoiled,  and  erasures  avoided  as  far  as  possible, 
and  the  style  and  strength  of  the  drawing  should  be  the  same  throughout.  It  is  an 
important  matter  that  an  easy  and  natural  appearance  should  be  given  to  the  map,  for,  as 
before  remarked ,  a  mere  rigid  adherence  to  conventional  signs  is  not  all  that  is  neces- 
sary; while  there  should  be  no  deviation  in  this  respect,  at  the  same  time  the  drafts- 
man should  strive  to  represent  the  country.  There  is  a  great  difference  with  regard  to 
this  among  topographers.  Two  perfectly  correct  charts  of  the  same  section  of  ground, 
executed  by  different  persons,  may  be  inked,  and  while  one  will  have  a  stiff  and 
ungraceful  look,  the  other  will  appear  artistic  and  natural,  giving  at  once  the 
impression  of  a  sincere  representation  of  the  country  surveyed. 

Office  work  should  not  be  commenced  until  the  topography  is  entirely  completed,  as 
no  inked  or  partially  inked  chart  should  ever  be  used  in  the  field.  Sometimes,  for  the 
special  examination  of  old  work,  or  for  the  insertion  of  some  recent  artificial  or  natural 
changes,  this  becomes  necessary.  There  is  always  a  risk  of  injuring  an  iuked  map  by 
exposure  to  the  weather  or  by  using  it  upon  a  plane  table. 

The  inking  should  commence  with  the  shore  lines,  high  and  low  water.  The  high 
water,  or  shore  line  proper,  should,  in  all  cases,  l>e  full  and  black,  the  heaviest  lines  on 


460  COAST  AND  GEODETIC  SURVEY  REPORT,  1897-98. 

the  sheet,  and  in  this,  as  in  all  the  rest  of  the  ink  work,  the  lines  of  the  survey  should 
be  strictly  adhered  to. 

The  topography  as  drawn  in  the  field  is  supposed  to  be  correct  when  the  chart  is 
finished,  and  no  office  amendments  or  changes  are  admissible.  The  low-water  line  is 
next  drawn,  not  so  full  as  the  former,  but  clear,  black,  and  uniform,  consisting  of  a 
dotted  line  for  sand  and  mud  and  the  conventional  sign  where  it  is  formed  by  shells, 
rocks,  or  coral  reefs. 

Grass  upon  flats,  or  shoals  covered  at  high  tide,  have  no  distinct  continuous  line  to 
mark  their  limits,  each  being  represented  in  its  proper  form  and  within  its  area  by  its 
conventional  sign  only,  but  the  shape  should  be  well  and  correctly  defined.  All  objects 
between  high  and  low  water,  covered  at  full  tide,  should  be  represented  less  boldly  than 
the  rest  of  the  map,  but  not  faintly  or  indefinitely. 

The  roads  should  next  be  inked  plainly  and  evenly,  and  their  sides  parallel,  except 
where  the  survey  shows  a  deviation  from  the  general  width.  Main  thoroughfares  when 
fenced  are  drawn  with  a  full  line,  subordinate  roads  where  fenced  should  be  shown  by 
the  usual  sign,  and  where  there  is  no  inclosure  a  line  of  dashes  should  indicate  the  road- 
side, and  then  should  follow  the  fences  and  houses.  In  drawing  the  latter  care  must  be 
taken  that  the  corners  and  angles  exhibit  a  sharp,  clear  outline,  which  adds  much  to  the 
appearance  of  the  map. 

The  general  skeleton  of  the  survey  being  now  completed,  the  contours  are  drawn 
with  a  bold,  uniform,  plain  red  line,  without  break,  over  all  the  other  work,  following 
accurately  the  full  range  of  level  of  each  of  the  contours  on  the  sheet. 

After  this  comes  the  general  filling  in,  by  conventional  signs,  of  sand,  marsh,  grass, 
cultivation,  orchards,  rocks,  hachures,  etc.  Some  practice  is  needed  to  execute  the  sand 
work  regularly  and  neatly.  It  should  never  be  hurriedly  done,  though  of  course 
rapidity  in  this  respect  follows  practice.  The  lines  representing  marsh,  and  the  delinea- 
tion of  grass  on  the  fast  land,  should  always  run  in  the  same  direction  over  the  whole 
sheet  and  be  parallel  to  the  top  of  the  sheet  and  the  title.  The  appended  drawings, 
Pis.  15,  1 6,  17,  and  18,  give  the  conventional  signs  as  adopted  by  and  now  used  in  the 
Coast  Survey. 

The  most  difficult  part  of  the  inking  for  a  beginner  is  the  lettering,  which  now 
follows,  and  for  which  samples  are  given  (PI.  19).  It  is  expected  that  every  topographer 
shall  have  learned  to  draw  sufficiently  well  to  ink  his  sheet  in  a  clear  and  distinct 
manner  and  letter  it  with  some  regard  to  neatness  and  graphic  effect,  as  the  appearance 
of  an  otherwise  well-inked  sheet  is  sometimes  marred  by  careless  or  indifferent  lettering. 

The  location  of  the  names  upon  the  sheet  should  be  such  as  not  to  cover  or  obliterate 
any  detail  or  feature  of  the  survey,  and  the  letters  should  be  put  in  neatly  and  grace- 
fully, and  in  point  of  size  and  form  according  to  the  specimens  furnished.  The  title 
should  finally  follow,  with  such  notes  as  may  be  necessary  to  explain  any  peculiarity  of 
the  sheet  or  survey.  This  title  and  lettering  should,  as  far  as  practicable,  be  so  placed, 
that  when  the  sheet  is  held  with  the  top  (usually  the  north  or  east  end  of  the  map)  from 
you  it  can  be  easily  read;  in  other  words,  as  nearly  parallel  to  the  top  or  upper  end  of 
the  sheet  as  the  nature  of  the  work  will  admit.  All  names  well  established  and  recog- 
nized in  a  neighborhood,  both  general  and  local,  should  be  collected  during  the  survey, 
and  their  correct  orthography  ascertained,  and  in  case  of  any  doubtful  or  disputed 
orthography  a  report  should  be  given  of  any  traditions  or  any  authorities  which  may 


APPENDIX  NO.  8.     PLANE  TABLE  MANUAL.  461 

bear  upon  the  subject.  No  illuminated  or  German  text,  old  English,  or  what  is  known 
as  "fancy  printing,"  should  be  indulged  in,  a  strict  adherence  to  simplicity  being  the 
greatest  ornament. 

The  minutes  of  the  parallels  of  latitude  and  meridians  of  longitude  should  be  marked 
in  figures  at  the  upper  and  right-hand  ends,  respectively,  the  degrees  on  the  center 
parallel  and  center  meridian  only. 

Where  the  .buoys  are  determined  by  the  topographer,  and  their  names,  colors, 
numbers,  or  kind  are  known,  they  should  be  lettered  upon  the  map. 

The  triangulation  points  should  also  be  lettered,  first  being  surrounded  by  a  small 
red  triangle.  Barns,  houses,  prominent  trees,  and  other  objects  determined  by  the 
plane-table  that  may  be  used  as  points  of  reference  in  making  additions  to  the  sheet 
subsequent  to  the  survey  should  be  indicated  by  a  small  blue  circle. 


NOTE. 

Plates  No.  20  to  No.  29  were  selected  from  a  collection  prepared  by  the  late  Assist- 
ant E.  Hergesheimer  to  illustrate  the  topographical  features  in  various  portions  of  the 
United  States.     The  full  collection  is  to  be  found  in  Appendix  14,  United  States  Coast 
and  Geodetic  Survey  Report,  1883. 
462 


Cs>a.tt  aiui  Geodetic  Survey  Report  1897-98   Appendix  8. 


Shoreline  Low  Water 


Oak 


Rocky  Ledgea 


Deciduous  and, 
Undergwwth 


Pine 


SrvdedlBarik. 


JPdbnetto 


Sand  and  Shingle 


Sand-Dunea 


Cacti, 


Topograpliical  Symbols 


Cuaxt  caul.  Geodetic  Survey  Report  1897-38   Appendix  8. 


No.  16. 


Salt  Marsh 


Cypress  Swamp 


Salt  Pond 


Grass 


t'r&sh  Marsh  and 
fresh  .Pond, 


Orchard 


Oyster  -Bed 


Ricelhkes  <t  Ditch fs 


Wooded,  M'trvh 


inayed  Marsh 


Curves  of  equal 

elevatum,  and 

intermfdiatr  curves 


Bel  Grass 


AW/, 


TopographicaQ  Symbols 


Const  arid  Geodetic  Survey  lleport  1897-98  Appendix  8 


Ho. 17 


Rapids 


Falls 


Dam. 


Kuft  Wia* 

f  proper  location,  ) 


Ferry 


Topographical  Station O 

Trumffidntivn,  Point A 

Dwettinff  JIauae. t 

Barn, 0 

Shed-  ajuLPen, D 

Ruins il; 

Windmill * 

Church it 

OIL 

C.cmetrry. aaa 

Pence, 

Public  Road. ^^^ 

Road  fenitd  on  one  /tuff, ~~~~ 

Rood,       '. .  .   . 


Topographieal  Syintols 


Coast  and  Geodetic  Survey  Report  1897  98  Appendix  8. 


Railroad  (eajch*  track ) i   i   .   .   t 

Railroad  (large.  Scale.). -   —   — 

Road  not  fenced •'7-^z^Z' 

Paffi  orTraH ,''--_--' 

Stone  Wall ._.._ ._....-. 

Hedge ___»_~. 

Embankment ******** 

Canal  andLock ,    , 

Known,  Altitude, 420  ft. 

*Approjc       n          (  njrprax  )  420  ft. 

Lighthouse,  frays  red  ) r .jk. 

Light-shipf   »        „    ) & 

Buoys  (  Can. Nun,  Spar  and  Bell  ) 

Red  and  Green, y 

Black / 

HorixoTital  Stripes   f 

Perpendicular  Stripes / 

Whistling t 

Lighted £ 

Mooring A 

Beacon,  ( Lighted,  rays  red  ) A 

Spindle,  or  Stake. i 

Anchorage ^ 


Rock  awash. ^ 

Sunken-  Rock  .... 


Topographical  Symbols 


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ENGRAV 

DIVISION 

CAPITOL 

HARBOR 

ISLANDS 

RIVERS 

SOUNDINGS 

DIRECTIONS 

*oints  POINTS 

'reeks  CREEKS 
bannels  CHANNELS 
loals  SHOALS 

PQRSTU 

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Coa.it  and.  Geodi*Lc  Survey  Report  1897  98    AppetvdLx  8. 


.  20 


'f^':*v?'t*V/^r*8   *~*.v 


Sparsely  settled,  To»rt,SaltMarsh^Pcn£  Woods ^Dttchjes.Fenoes, and.  TTrideftned.  Roajds( Brrcnswvck, 


Coast  and  Geodetic  Survey  Re-port  1837-98   Appendix  8. 


No.  21 


Rtairoeulfi,GinaJs,fnmi  liridf/rs, Rocky  C&ffs,jfutrirer drift,  Waters-worn  rncks Mixed  woods  over  hULcm-vcs. 


f'mint  Hint   <;,;,<l,'tit    Survfy  Hf/HH'l   Itt'J~  W    A/ififfldi^  8. 


No.  22 


Heavy  OaJ<  Woocfx.  RecLtiinifd  Mtirxh  ami 


Count  nnd  flcoili'tic  Stifvcy  Hftxirt  !H'J /    '.If,    Appc.nd;.\ 


l^-Bfc  11^-^= u?'~*~  jE^-*11   Ji.     *"»  ^^^    4!*  ^=^^u^=y.  TT  jr.    ,»•: 

.,;, 


- 

•  - 


r     U     ^  •*&  A^lft.-*;^: 


""^MWaiiiu.^^-    -.^T-'-'-'-V""^".'^.';-?    '."    ^*&|  ^Ik  -^e/Ut*: 


^/^/r/  J)iJ.t.'/if<..  ( Siuitsze.  Jiiver) 


(\Kifit  /mil 


:y  Kt'i>'"'<  HW7-3H    Appendix  8. 


No. 


drift,  ba,n,k,s.  with,  bou,lder-Si  set  free;  a*ui  scrub  (lecidu-oiis  woods.  (Guy  HeaudL) 


No.  25 


-Ui'  Slit  v,'Y  Ht'fMfl  HW7  '.'«    ,1/y>m<//.r 


Scwirl  Bea>ch  with], vw  Dnru?s,  FrcstiWater  Pond*  Meadow  Gi-(iss,  Sr.ir/e  Brush  and.  A 

(S.    Coast. 


Coast  and  Geodetic  Survey  Report.  1837-V8  Appetuli.v  8 


Blocking  of'  Cities.  -Lfi7-<jt>  BiiUdings,  SvJncrbcm  Vittas  an,d Grounds.  Fresh  Marsh-  <-?fei-vporL,ft.I.> 


unit  dcinli-itr  Stirvry  ll,-fH,rt  Ift'.i?  ,98    AfipfiuUx.  8. 


No.  2 7 


V-o.s •;.  <n    a.''  So/'t  Xti-tj.ti.fn-, I    li'.ii-k     nini    C/'//<-/u    (Santa,  Cr-ux?,  CoL.) 

TM*  «^MWI»  f«rcin  ui  PMOTO^ITHO.  wAiniworo**.  r 


Coast  and-  Geodetic  Survey  Report  1897-98.  Appendix  8. 


No.  30. 


Hill  Curves  for  every  20  feet  difference  of  level.  Scale 


Slope. 

Proportion 
of 
Height  to  Base. 

Length  of  Base 
1  footer  Height 
(  in  feet.) 

Length^  Base 
20  feet  of  Height 
(in  feet.) 

Length  of  Base 
2O  feetof  Height 

(  in  metres  > 

r 

1  to  57 

57.  29 

1145  .  8 

349.1 

2* 

1  to  29 

28.64 

572.8 

174.  5 

3* 

1  to  19 

19.06 

381.6 

116.  3 

4* 

1  to  14 

14.  30 

286.0 

87.  1 

5° 

1  toll 

11.43 

228.6 

69.7 

10T 

1  to  6 

5.67 

113.4 

34.6 

1ST 

1  to  4 

3.73 

74.6 

22.  7 

20' 

1  to  3 

2  .75 

55.0 

16.7 

25* 

1  to  2 

2  .  14 

42.8 

13.1 

30* 

1  to  1.7 

1.73 

34.6 

10.  5 

35° 

1  to  1.4 

1.43 

28.6 

8  .7 

40* 

1  to  1.2 

1  .19 

23.8 

7.  2 

45' 

1  to  1 

1  .00 

20.0 

6.1 

50* 

1  to  0.8 

0.84 

16.8 

5.1 

55' 

1  to  0.7 

0.70 

14.  0 

4.3 

60* 

1  to  0.6 

0.  58 

11.6 

3.6 

UJ 


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Coast  and  Geodetic  Siu-vey  Report  lftV7-<18   Appendix  8. 


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